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

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)`

Prove the following identities:

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

Prove the following identities:

`(1+ sin A)/(cosec A - cot A) - (1 - sin A)/(cosec A + cot A) = 2(1 + cot A)`

Prove the following identities:

`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`

Prove that:

(sec A − tan A)² (1 + sin A) = (1 − sin A)

Prove that:

`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`

Prove that:

`tanA/(1 - cotA) + cotA/(1 - tanA) = secA  "cosec"  A + 1`

Prove that:

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

Prove that:

2 sin² A + cos⁴ A = 1 + sin⁴ A 

Prove that:

`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`

Prove that:

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

Prove that:

(1 + tan A . tan B)² + (tan A – tan B)² = sec² A sec² B

Prove that:

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

If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x² + y² = m² + n²