English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

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

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

[Hint : Simplify LHS and RHS separately.]

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

`sqrt((1+sinA)/(1-sinA)) = secA + tanA`

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

`(cos A-sinA+1)/(cosA+sinA-1)=cosecA+cotA ` using the identity cosec² A = 1 cot² A.

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 - cos^2 A) cosec^2 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 theta cosec theta`

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 identity.

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