English

`Sin^2 Theta + 1/((1+Tan^2 Theta))=1` - Mathematics

Advertisements
Advertisements

Question

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

Solution

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

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

    = `sin^2 theta + cos^2 theta`

    = 1

   =RHS

shaalaa.com
  Is there an error in this question or solution?
Chapter 8: Trigonometric Identities - Exercises 1

APPEARS IN

RS Aggarwal Mathematics [English] Class 10
Chapter 8 Trigonometric Identities
Exercises 1 | Q 3.1

RELATED QUESTIONS

Prove that:

sec2θ + cosec2θ = sec2θ x cosec2θ


 Evaluate sin25° cos65° + cos25° sin65°


Prove the following trigonometric identities.

`sin theta/(1 - cos theta) =  cosec theta + cot theta`


Prove the following trigonometric identities.

`(cot A + tan B)/(cot B + tan A) = cot A tan B`


if `a cos^3 theta + 3a cos theta sin^2 theta = m, a sin^3 theta + 3 a cos^2 theta sin theta = n`Prove that `(m + n)^(2/3) + (m - n)^(2/3)`


Given that:
(1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos α) (1 − cos β) (1 − cos γ)

Show that one of the values of each member of this equality is sin α sin β sin γ


Prove the following identities:

`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (1 + cosA)/sinA`


Prove that:

`tanA/(1 - cotA) + cotA/(1 - tanA) = secA cosecA + 1`


Prove the following identities:

`(sinA - cosA + 1)/(sinA + cosA - 1) = cosA/(1 - sinA)`


Write the value of \[\cot^2 \theta - \frac{1}{\sin^2 \theta}\] 


If a cos θ + b sin θ = 4 and a sin θ − b sin θ = 3, then a2 + b2


Prove the following identity : 

`((1 + tan^2A)cotA)/(cosec^2A) = tanA`


Prove the following identity  :

`(1 + cotA)^2 + (1 - cotA)^2 = 2cosec^2A`


prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`


Prove that tan2Φ + cot2Φ + 2 = sec2Φ.cosec2Φ.


Prove that ( 1 + tan A)2 + (1 - tan A)2 = 2 sec2A


If x = h + a cos θ, y = k + b sin θ. 
Prove that `((x - h)/a)^2 + ((y - k)/b)^2 = 1`.


Prove the following identities.

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


If `sqrt(3)` sin θ – cos θ = θ, then show that tan 3θ = `(3tan theta - tan^3 theta)/(1 - 3 tan^2 theta)`


Choose the correct alternative:

sec2θ – tan2θ =?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×