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

Prove the following identities:

`secA/(secA + 1) + secA/(secA - 1) = 2cosec^2A`

Prove the following identities:

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

Prove the following identities:

`cot^2A/(cosecA + 1)^2 = (1 - sinA)/(1 + sinA)`

Prove the following identities:

`(1 + sinA)/cosA + cosA/(1 + sinA) = 2secA`

Prove the following identities:

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

Prove the following identities:

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

Prove the following identities:

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

Prove the following identities:

`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2A * cos^2B)`

Prove the following identities:

`(sintheta - 2sin^3theta)/(2cos^3theta - costheta) = tantheta`

Prove the following identities:

`sinA/(1 + cosA) = cosec A - cot A`

Prove the following identities:

`cosA/(1 - sinA) = sec A + tan A`

Prove the following identities:

`(sinAtanA)/(1 - cosA) = 1 + secA`

Prove the following identities:

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

Prove the following identities:

`sqrt((1 + sinA)/(1 - sinA)) = sec A + tan A`

Prove the following identities:

`sqrt((1 - cosA)/(1 + cosA)) = cosec A - cot A`

Prove the following identities:

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

Prove the following identities:

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

Prove the following identities:

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

Prove the following identities:

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

Prove the following identities:

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