Advertisements
Advertisements
Question
Prove the following identity :
`(1 - cos^2θ)sec^2θ = tan^2θ`
Advertisements
Solution
`(1 - cos^2θ)sec^2θ = tan^2θ`
Consider L.H.S = `sin^2θ1/cos^2θ`
= `tan^2θ` = RHS
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
if cos A + cos2 A = 1, prove that sin2 A + sin4 A = 1
Prove the following identities:
cosec A(1 + cos A) (cosec A – cot A) = 1
`(tan^2theta)/((1+ tan^2 theta))+ cot^2 theta/((1+ cot^2 theta))=1`
`(tan A + tanB )/(cot A + cot B) = tan A tan B`
If cosec θ = 2x and \[5\left( x^2 - \frac{1}{x^2} \right)\] \[2\left( x^2 - \frac{1}{x^2} \right)\]
If x = a sec θ cos ϕ, y = b sec θ sin ϕ and z = c tan θ, then\[\frac{x^2}{a^2} + \frac{y^2}{b^2}\]
Find the value of ( sin2 33° + sin2 57°).
Prove that sin2 5° + sin2 10° .......... + sin2 85° + sin2 90° = `9 1/2`.
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
Prove that (1 – cos2A) . sec2B + tan2B (1 – sin2A) = sin2A + tan2B.
