Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board chapter 2 - Trigonometry - 1 [Latest edition]

Find the trigonometric function of :

0°

Find the trigonometric function of :

30°

Find the trigonometric function of:

45°

Find the trigonometric function of :

60°

Find the trigonometric function of : 

150°

Find the trigonometric functions of :

180°

Find the trigonometric function of :

210°

Find the trigonometric function of :

300°

Find the trigonometric functions of :

330°

Find the trigonometric functions of :

−30°

Find the trigonometric functions of :

−45°

Find the trigonometric functions of :

−60°

Find the trigonometric functions of :

− 90°

Find the trigonometric functions of : 

−120°

Find the trigonometric functions of :

−225°

Find the trigonometric functions of :

−240°

Find the trigonometric functions of :

−270°

Find the trigonometric functions of :

−315°

State the signs of tan 380°

State the signs of cot 230°

State the signs of sec 468°

State the signs of cos4^c and cos4°. Which of these two functions is greater?

State the quadrant in which θ lies if :

sin θ < 0 and tan θ > 0

State the quadrant in which θ lies if :

cos θ < 0 and tan θ > 0

Evaluate the following:

sin 30° + cos 45° + tan 180°

Evaluate the following : 

cosec 45° + cot 45° + tan 0°

Evaluate the following : 

sin 30° × cos 45° × tan 360°

Find all trigonometric functions of angle in standard position whose terminal arm passes through point (3, −4).

If cos θ = `12/13`, 0 < θ < `pi/2`, find the value of `(sin^2theta - cos^2theta)/(2sinthetacostheta), 1/(tan^2theta)`

Using tables evaluate the following :

4 cot 45° – sec² 60° + sin 30°

Using tables evaluate the following :

`cos^2 0 + cos^2  pi/6 + cos^2  pi/3 + cos^2  pi/2`

Find the other trigonometric functions:

If cos θ = `-3/5` and 180° < θ < 270°.

Find the other trigonometric functions if sec A = `-25/7` and A lies in the second quadrant.

Find the other trigonometric functions:

If cot x = `3/4`, x lies in the third quadrant.

Find the other trigonometric functions:

If tan x = `(-5)/12`, x lies in the fourth quadrant.

If 2 sinA = 1 = `sqrt(2)` cosB and `pi/2` < A < `pi`, `(3pi)/2` < B < `2pi`, then find the value of `(tan"A" + tan"B")/(cos"A" - cos"B")`

If `sin"A"/3 = sin"B"/4 = 1/5` and A, B are angles in the second quadrant then prove that 4cosA + 3cosB = – 5.

If tanθ = `1/2`, evaluate `(2sin theta + 3cos theta)/(4cos theta + 3sin theta)`

Eliminate θ from the following: 

x = 3secθ , y = 4tanθ

Eliminate θ from the following : 

x = 6cosecθ, y = 8cotθ

Eliminate θ from the following :

x = 4cosθ − 5sinθ, y = 4sinθ + 5cosθ

Eliminate θ from the following :

x = 5 + 6cosecθ, y = 3 + 8cotθ

Eliminate θ from the following:

2x = 3 − 4 tan θ, 3y = 5 + 3 sec θ

If 2 sin²θ + 3 sin θ = 0, find the permissible values of cos θ.

If 2cos²θ − 11cosθ + 5 = 0 then find possible values of cosθ.

Find the acute angle θ such that 2 cos²θ = 3 sin θ.

Find the acute angle θ such that 5tan²θ + 3 = 9secθ.

Find sinθ such that 3cosθ + 4sinθ = 4

If cosecθ + cotθ = 5, then evaluate secθ.

If cotθ = `3/4` and π < θ < `(3pi)/2` then find the value of 4cosecθ + 5cosθ.

Find the Cartesian co-ordinates of points whose polar coordinates are :

(3, 90°)

Find the Cartesian co-ordinates of points whose polar coordinates are :

(1,180°)

Find the polar coordinates of points whose cartesian coordinates are:

(5, 5)

Find the polar coordinates of points whose cartesian coordinates are :

`(1, sqrt(3))`

Find the polar co-ordinates of points whose Cartesian co-ordinates are:

(–1, –1)

Find the polar co-ordinates of points whose Cartesian co-ordinates are:

`(- sqrt(3), 1)`

Find the value of `sin  (19pi^"c")/3`.

Find the value of :

cos 1140°

Find the values of:

`cot  (25pi^"c")/3`

Prove the following identities:

`(1 + tan^2 "A") + (1 + 1/tan^2"A") = 1/(sin^2 "A" - sin^4"A")`

Prove the following identities: 

(cos²A – 1) (cot²A + 1) = −1

Prove the following identities:

(sinθ + sec θ)² + (cosθ + cosec θ)² = (1 + cosecθ sec θ)² 

Prove the following identities:

(1 + cot θ – cosec θ)(1 + tan θ + sec θ) = 2

Prove the following identities:

`tan^3theta/(1 + tan^2theta) + cot^3theta/(1 + cot^2theta` = secθ cosecθ – 2sinθ cosθ

Prove the following identities:

`1/(sectheta + tantheta) - 1/costheta = 1/costheta - 1/(sectheta - tantheta)`

Prove the following identities:

`sintheta/(1 + costheta) + (1 + costheta)/sintheta` = 2cosecθ

Prove the following identity:

`tantheta/(sectheta - 1) = (sectheta + 1)/tantheta`

Prove the following identities:

`cottheta/("cosec"  theta - 1) = ("cosec"  theta + 1)/cot theta`

Prove the following identities:

(sec A + cos A)(sec A − cos A) = tan²A + sin²A

Prove the following identity:

1 + 3cosec²θ cot²θ + cot⁶θ = cosec⁶θ

Prove the following identity:

`(1 - sec theta + tan theta)/(1 + sec theta - tan theta) = (sec theta + tan theta - 1)/(sec theta + tan theta + 1)`

Select the correct option from the given alternatives:

The value of the expression cos1°. cos2°. cos3° … cos179° =

Select the correct option from the given alternatives: 

`tan"A"/(1 + sec"A") + (1 + sec"A")/tan"A"` is equal to

Select the correct option from the given alternatives:

If α is a root of 25cos²θ + 5cosθ – 12 = 0, `pi/2` < α < π, then sin2α is equal to

Select the correct option from the given alternatives:

If θ = 60°, then `(1 + tan^2theta)/(2tantheta)` is equal to

Select the correct option from the given alternatives:

If secθ = m and tanθ = n, then `1/"m"{("m + n") + 1/(("m + n"))}` is equal to

Select the correct option from the given alternatives:

If cosecθ + cotθ = `5/2`, then the value of tanθ is

Select the correct option from the given alternatives:

`1 - sin^2theta/(1 + costheta) + (1 + costheta)/sintheta - sintheta/(1 - costheta)` equals

Select the correct option from the given alternatives:

If cosecθ − cotθ = q, then the value of cot θ is

Select the correct option from the given alternatives:

The cotangent of the angles `pi/3, pi/4 and pi/6` are in

Select the correct option from the given alternatives:

The value of tan1°.tan2°tan3°..... tan89° is equal to

Answer the following:

Find the trigonometric functions of :

90°

Find the trigonometric functions of 120°.

Find the trigonometric functions of 225°.

Answer the following:

Find the trigonometric functions of :

240°

Answer the following:

Find the trigonometric functions of :

270°

Answer the following:

Find the trigonometric functions of :

315°

Find the trigonometric functions of : 

−120°

Answer the following:

Find the trigonometric functions of :

−150°

Answer the following:

Find the trigonometric functions of :

−180°

Answer the following:

Find the trigonometric functions of :

−210°

Answer the following:

Find the trigonometric functions of :

−300°

Answer the following:

Find the trigonometric functions of :

−330°

Answer the following:

State the signs of cosec 520°

Answer the following:

State the signs of cot 1899°

Answer the following:

State the signs of sin 986°

Answer the following:

State the quadrant in which θ lies if tan θ < 0 and sec θ > 0

Answer the following:

State the quadrant in which θ lies if sin θ < 0 and cos θ < 0

Answer the following:

State the quadrant in which θ lies if sin θ > 0 and tan θ < 0

Answer the following:

Which is greater sin(1856°) or sin(2006°)?

Answer the following:

Which of the following is positive? sin(−310°) or sin(310°)

Answer the following:

Show that 1 − 2sinθ cosθ ≥ 0 for all θ ∈ R.

Answer the following:

Show that tan²θ + cot²θ ≥ 2 for all θ ∈ R

Answer the following:

If sinθ = `(x^2 - y^2)/(x^2 + y^2)` then find the values of cosθ, tanθ in terms of x and y.

Answer the following:

If sec θ = `sqrt(2)` and `(3pi)/2 < theta < 2pi` then evaluate `(1 + tantheta + "cosec"theta)/(1 + cottheta - "cosec"theta)`

Prove the following:  

sin²A cos²B + cos²A sin²B + cos²A cos²B + sin²A sin²B = 1

Prove the following:

`((1 + cot theta + tan theta)(sin theta - costheta)) /(sec^3theta - "cosec"^3theta)`= sin²θ cos²θ

Prove the following:

`(tan theta + 1/costheta)^2 + (tan theta - 1/costheta)^2 = 2((1 + sin^2theta)/(1 - sin^2theta))`

Prove the following:

2 sec²θ – sec⁴θ – 2cosec²θ + cosec⁴θ = cot⁴θ – tan⁴θ

Prove the following:

sin⁴θ + cos⁴θ = 1 – 2 sin²θ cos²θ

Prove the following:

2(sin⁶θ + cos⁶θ) – 3(sin⁴θ + cos⁴θ) + 1 = 0

Prove the following:

cos⁴θ − sin⁴θ +1= 2cos²θ

Prove the following:

sin⁴θ +2sin²θ . cos²θ = 1 − cos⁴θ

Prove the following:

`(sin^3theta + cos^3theta)/(sintheta + costheta) + (sin^3theta - cos^3theta)/(sintheta - costheta)` = 2

Prove the following:

tan²θ − sin²θ = sin⁴θ sec²θ

Prove the following:

(sinθ + cosecθ)² + (cosθ + secθ)² = tan²θ + cot²θ + 7

Prove the following:

sin⁸θ − cos⁸θ = (sin²θ − cos²θ) (1 − 2 sin²θ cos²θ)

Prove the following:

sin⁶A + cos⁶A = 1 − 3sin²A + 3 sin⁴A

Prove the following:

(1 + tanA · tanB)² + (tanA − tanB)² = sec²A · sec²B

Prove the following:

`(1 + cot  +  "cosec" theta)/(1 - cot  +  "cosec" theta) = ("cosec" theta  + cottheta - 1)/(cottheta - "cosec"theta + 1)`

Prove the following:

`(tantheta + sectheta - 1)/(tantheta + sectheta + 1) = tantheta/(sec theta + 1)`

Prove the following:

`("cosec"theta + cottheta - 1)/( "cosec"theta + cot theta + 1) =(1-sintheta)/costheta`

Prove the following:

`("cosec"theta + cottheta + 1)/(cottheta + "cosec" theta - 1) = cottheta/("cosec"theta - 1)`