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

Prove the following identities:

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

Prove the following identities:

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

Prove the following identities:

(1 – tan A)² + (1 + tan A)² = 2 sec²A

Prove the following identities:

cosec⁴ A – cosec² A = cot⁴ A + cot² A

Prove the following identities:

cosec A(1 + cos A) (cosec A – cot A) = 1

Prove the following identities:

sec²A + cosec²A = sec²A . cosec²A

Prove the following identities:

`((1 + tan^2A)cotA)/(cosec^2A) = tan A`

Prove the following identities:

cot² A – cos² A = cos² A . cot² A

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`