English Medium कक्षा १० - CBSE Question Bank Solutions

 Evaluate sin25° cos65° + cos25° sin65°

9 sec² A − 9 tan² A = ______.

(1 + tan θ + sec θ) (1 + cot θ − cosec θ) = ______.

(secA + tanA) (1 − sinA) = ______.

`(1+tan^2A)/(1+cot^2A)` = ______.

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

`(cosec  θ  – cot θ)^2 = (1-cos theta)/(1 + cos theta)`

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

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

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

`(tan theta)/(1-cot theta) + (cot theta)/(1-tan theta) = 1+secthetacosectheta`

[Hint: Write the expression in terms of sinθ and cosθ]

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`