English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

Prove the following trigonometric identities.

sec A (1 − sin A) (sec A + tan A) = 1

Prove the following trigonometric identities.

tan² θ − sin² θ = tan² θ sin² θ

Prove the following trigonometric identities.

(1 + tan²θ) (1 − sinθ) (1 + sinθ) = 1

Prove the following trigonometric identities.

sin² A cot² A + cos² A tan² A = 1

Prove the following trigonometric identities.

`cot theta - tan theta = (2 cos^2 theta - 1)/(sin theta cos theta)`

Prove the following trigonometric identities.

`tan theta - cot theta = (2 sin^2 theta - 1)/(sin theta cos theta)`

Prove the following trigonometric identities.

`(cos^2 theta)/sin theta - cosec theta +  sin theta  = 0`

Prove the following trigonometric identities.

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

Prove the following trigonometric identities.

`(1 + sin θ)/cos θ+ cos θ/(1 + sin θ) = 2 sec θ`

Prove the following trigonometric identities

`((1 + sin theta)^2 + (1 + sin theta)^2)/(2cos^2 theta) =  (1 + sin^2 theta)/(1 - sin^2 theta)`

Prove the following trigonometric identities

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

Prove the following trigonometric identities.

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

Prove the following trigonometric identities.

`tan θ/(1 - cot θ) + cot θ/(1 - tan θ) = 1 + tan θ + cot θ`

Prove the following trigonometric identities.

sec⁶ θ = tan⁶ θ + 3 tan² θ sec² θ + 1

Prove the following trigonometric identities

cosec⁶θ = cot⁶θ + 3 cot²θ cosec²θ + 1

Prove the following trigonometric identities.

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

Prove the following trigonometric identities.

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

Prove the following trigonometric identities.

`(sec A - tan A)/(sec A + tan A) = (cos^2 A)/(1 + sin A)^2`

Prove the following trigonometric identities.

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

Prove the following trigonometric identity:

`sqrt((1 + sin A)/(1 - sin A)) = sec A + tan A`