English

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

Advertisements
Advertisements

Question

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

Solution

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

       =`1/sec^2 theta + 1/(cosec^2 theta)`

       =` cos^2 theta + sin^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 3.2

RELATED QUESTIONS

 Evaluate sin25° cos65° + cos25° sin65°


Prove the following identities, where the angles involved are acute angles for which the expressions are defined:

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


If `x/a=y/b = z/c` show that `x^3/a^3 + y^3/b^3 + z^3/c^3 = (3xyz)/(abc)`.


Evaluate without using trigonometric tables:

`cos^2 26^@ + cos 64^@ sin 26^@ + (tan 36^@)/(cot 54^@)`


Prove the following trigonometric identities.

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


Prove that:

`(tanA + 1/cosA)^2 + (tanA - 1/cosA)^2 = 2((1 + sin^2A)/(1 - sin^2A))`


If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m2 + n2) cos2 B = n2.


Show that none of the following is an identity:
(i) `cos^2theta + cos theta =1`


If `sin theta = x , " write the value of cot "theta .`


Prove the following identity : 

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


If x = acosθ , y = bcotθ , prove that `a^2/x^2 - b^2/y^2 = 1.`


If `asin^2θ + bcos^2θ = c and p sin^2θ + qcos^2θ = r` , prove that (b - c)(r - p) = (c - a)(q - r)


If sec θ = `25/7`, then find the value of tan θ.


Find the value of ( sin2 33° + sin2 57°).


Evaluate:
`(tan 65°)/(cot 25°)`


Prove that sec θ. cosec (90° - θ) - tan θ. cot( 90° - θ ) = 1.


Proved that cosec2(90° - θ) - tan2 θ = cos2(90° - θ)  +  cos2 θ.


Prove the following identities: cot θ - tan θ = `(2 cos^2 θ - 1)/(sin θ cos θ)`.


Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.


Prove that (sec θ + tan θ) (1 – sin θ) = cos θ


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×