English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

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`

Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.

Prove the following trigonometric identities:

(1 – cos² A) cosec² A = 1

Prove the following trigonometric identities:

(1 + cot² A) sin² A = 1

Prove the following trigonometric identities.

tan²θ cos²θ = 1 − cos²θ

Prove the following trigonometric identities.

`"cosec" theta sqrt(1 - cos^2 theta) = 1`

Prove the following trigonometric identities.

(sec² θ − 1) (cosec² θ − 1) = 1

Prove the following trigonometric identities.

`tan theta + 1/tan theta` = sec θ.cosec θ

Prove the following trigonometric identities

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

Prove the following trigonometric identities:

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

Prove the following trigonometric identities.

`cos^2 A + 1/(1 + cot^2 A) = 1`

Prove the following trigonometric identities.

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

Prove the following trigonometric identities.

`sqrt((1 - cos theta)/(1 + cos theta)) = cosec theta - cot theta`

Prove the following trigonometric identities:

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

Prove the following trigonometric identities:

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

Prove the following trigonometric identities.

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

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 + tan² θ) (1 − sin θ) (1 + sin θ) = 1

Prove the following trigonometric identities:

sin² A cot² A + cos² A tan² A = 1