Prove that Sec2 (90° - θ) + Tan2 (90° - θ) = 1 + 2 Cot2 θ.

Prove that sec² (90° - θ) + tan² (90° - θ) = 1 + 2 cot² θ.

Sum

LHS = sec² (90° - θ) + tan² (90° - θ)

= cosec²θ + cot²θ

= 1 + cot²θ + cot²θ

= 1 + 2cot²θ

= RHS
Hence proved.

shaalaa.com

Is there an error in this question or solution?

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

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

Prove that:

`sqrt(sec^2A + cosec^2A) = tanA + cotA`

From the figure find the value of sinθ.

Without using trigonometric table , evaluate :

`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`

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

Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.

Prove that sin²5° + sin²10° .......... + sin²85° + sin²90° = `9 1/2`.

If (sin α + cosec α)² + (cos α + sec α)² = k + tan²α + cot²α, then the value of k is equal to

Prove that `(cos(90^circ - A))/(sin A) = (sin(90^circ - A))/(cos A)`.

`sqrt((1 - cos^2theta) sec^2 theta) = tan theta`