(English Medium) ICSE Class 10 - CISCE Question Bank Solutions

If A + B = 90°, show that sec² A + sec² B = sec² A. sec² B.

If A + B = 90°, show that `(sin B + cos A)/sin A = 2tan B + tan A.`

Prove the following identities: sec² θ + cosec² θ = sec² θ cosec² θ.

Prove the following identities: cot θ - tan θ = `(2 cos^2 θ - 1)/(sin θ cos θ)`.

Prove the following identities:
`1/(sin θ + cos θ) + 1/(sin θ - cos θ) = (2sin θ)/(1 - 2 cos^2 θ)`.

Prove the following identities:

`(1 - tan^2 θ)/(cot^2 θ - 1) = tan^2 θ`.

Prove that the following identities:
Sec A( 1 + sin A)( sec A - tan A) = 1.

Prove that: sin⁴ θ + cos⁴θ = 1 - 2sin²θ cos² θ.

Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.

Prove that identity:
`(sec A - 1)/(sec A + 1) = (1 - cos A)/(1 + cos A)`

Prove that:  `1/(sec θ - tan θ) = sec θ + tan θ`.

Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.

Prove that `(tan θ + sin θ)/(tan θ - sin θ) = (sec θ + 1)/(sec θ - 1)`

Prove that: `(1 + cot^2 θ/(1 + cosec θ)) = cosec θ`.

Prove that: `(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(sin^2 A - cos^2 A)`.

Prove that: `1/(cosec"A" - cot"A") - 1/sin"A" = 1/sin"A" - 1/(cosec"A" + cot"A")`

Prove that: sin⁶θ + cos⁶θ = 1 - 3sin²θ cos²θ. 

Prove that:
`(cos^3 θ + sin^3 θ)/(cos θ + sin θ) + (cos^3 θ - sin^3 θ)/(cos θ - sin θ) = 2`

Prove that sin² 5° + sin² 10° .......... + sin² 85° + sin² 90° = `9 1/2`.

Prove that : `tan"A"/(1 - cot"A") + cot"A"/(1 - tan"A") = sec"A".cosec"A" + 1`.