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

Prove the following identities:

(cosec A + sin A) (cosec A – sin A) = cot² A + cos² A

Prove the following identities:

(sec A – cos A) (sec A + cos A) = sin² A + tan² A 

Prove the following identities:

(cos A + sin A)² + (cos A – sin A)² = 2

Prove the following identities:

(cosec A – sin A) (sec A – cos A) (tan A + cot A) = 1

Prove the following identities:

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

Prove the following identities:

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

Prove the following identities:

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

Prove the following identities:

(sin A + cosec A)² + (cos A + sec A)² = 7 + tan² A + cot² A

Prove the following identities:

sec² A . cosec² A = tan² A + cot² A + 2

Prove the following identities:

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

Prove the following identities:

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

Prove the following identities:

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

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)`