English Medium इयत्ता १० - CBSE Question Bank Solutions

Prove the following trigonometric identities.

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

Prove the following trigonometric identities

tan² A + cot² A = sec² A cosec² A − 2

Prove the following trigonometric identities.

`(1 - tan^2 A)/(cot^2 A -1) = tan^2 A`

Prove the following trigonometric identities.

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

Prove the following trigonometric identities.

`(cos theta)/(cosec theta + 1) + (cos theta)/(cosec theta - 1) = 2 tan theta`

Prove the following trigonometric identities.

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

Prove the following trigonometric identities.

`(tan^3 theta)/(1 + tan^2 theta) + (cot^3 theta)/(1 + cot^2 theta) = sec theta cosec theta - 2 sin theta cos theta`

Prove the following trigonometric identities.

if `T_n = sin^n theta + cos^n theta`, prove that `(T_3 - T_5)/T_1 = (T_5 - T_7)/T_3`

Prove the following trigonometric identities.

`[tan θ + 1/cos θ]^2 + [tan θ - 1/cos θ]^2 = 2((1 + sin^2 θ)/(1 - sin^2 θ))`

Prove the following trigonometric identities.

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

Prove the following trigonometric identities.

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

Prove the following trigonometric identities.

(sec A + tan A − 1) (sec A − tan A + 1) = 2 tan A

Prove the following trigonometric identities.

(1 + cot A − cosec A) (1 + tan A + sec A) = 2

Prove the following trigonometric identities.

(cosec θ − sec θ) (cot θ − tan θ) = (cosec θ + sec θ) ( sec θ cosec θ − 2)

Prove the following trigonometric identities.

(sec A − cosec A) (1 + tan A + cot A) = tan A sec A − cot A cosec A

Prove the following trigonometric identities.

`(cos A cosec A - sin A sec A)/(cos A + sin A) = cosec A - sec A`

Prove the following trigonometric identities.

`sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A + 1) = 1`

Prove the following trigonometric identities.

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

Prove the following trigonometric identities

sec⁴ A(1 − sin⁴ A) − 2 tan² A = 1

Prove the following trigonometric identities.

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