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

Prove the following identities:

`1/(cosA + sinA) + 1/(cosA - sinA) = (2cosA)/(2cos^2A - 1)`

Prove the following identities:

`cosecA - cotA = sinA/(1 + cosA)`

Prove the following identities:

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

Prove the following identities:

`(1 - cosA)/sinA + sinA/(1 - cosA)= 2cosecA`

Prove the following identities:

`cotA/(1 - tanA) + tanA/(1 - cotA) = 1 + tanA + cotA`

Prove the following identities:

`cosA/(1 + sinA) + tanA = secA`

Prove the following identities:

`sinA/(1 - cosA) - cotA = cosecA`

Prove the following identities:

`(sinA - cosA + 1)/(sinA + cosA - 1) = cosA/(1 - sinA)`

Prove the following identities:

`sqrt((1 + sinA)/(1 - sinA)) = cosA/(1 - sinA)`

Prove the following identities:

`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`

Prove the following identities:

`(1 + (secA - tanA)^2)/(cosecA(secA - tanA)) = 2tanA`

Prove the following identities:

`((cosecA - cotA)^2 + 1)/(secA(cosecA - cotA)) = 2cotA`

Prove the following identities:

`cot^2A((secA - 1)/(1 + sinA)) + sec^2A((sinA - 1)/(1 + secA)) = 0`

Prove the following identities:

`(1 - 2sin^2A)^2/(cos^4A - sin^4A) = 2cos^2A - 1`

Prove the following identities:

sec⁴ A (1 – sin⁴ A) – 2 tan² A = 1

Prove the following identities:

cosec⁴ A (1 – cos⁴ A) – 2 cot² A = 1

Prove the following identities:

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

If sin A + cos A = p and sec A + cosec A = q, then prove that : q(p² – 1) = 2p.

If x = a cos θ and y = b cot θ, show that:

`a^2/x^2 - b^2/y^2 = 1` 

If sec A + tan A = p, show that:

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