Prove the following identities: cot2A(cosecA+1)2=1-sinA1+sinA

Prove the following identities:

`cot^2A/(cosecA + 1)^2 = (1 - sinA)/(1 + sinA)`

Sum

R.H.S. = `(1 - sinA)/(1 + sinA)`

= `(1 - 1/(cosecA))/(1 + 1/(cosecA))`

= `(cosecA - 1)/(cosecA + 1)`

= `(cosecA - 1)/(cosecA + 1) xx (cosecA + 1)/(cosecA + 1)`

= `(cosec^2A - 1)/(cosecA + 1)^2 = cot^2A/(cosecA + 1)^2` ...(∵ cosec² A – 1 = cot² A)

= L.H.S.

shaalaa.com

Is there an error in this question or solution?

Prove that (cosec A – sin A)(sec A – cos A) sec² A = tan A.

Prove the following trigonometric identities.

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

If x = a sin θ and y = bcos θ , write the value of`(b^2 x^2 + a^2 y^2)`

If `sec theta + tan theta = x," find the value of " sec theta`

What is the value of (1 − cos² θ) cosec² θ?

(sec A + tan A) (1 − sin A) = ______.

Prove the following identity :

`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`

Prove that `(cot "A" + "cosec A" - 1)/(cot "A" - "cosec A" + 1) = (1 + cos "A")/sin "A"`

Prove the following identities.

`(1 - tan^2theta)/(cot^2 theta - 1)` = tan² θ

If 1 + sin²α = 3 sinα cosα, then values of cot α are ______.