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

Prove the following identity :

secA(1 + sinA)(secA - tanA) = 1

Prove the following identity :

cosecθ(1 + cosθ)(cosecθ - cotθ) = 1

Prove the following identity :

`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`

Prove the following identity:

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

Prove the following identity :

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

Prove the following identity : 

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

Prove the following identity : 

`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`

Prove the following identity :

`(1 - tanA)^2 + (1 + tanA)^2 = 2sec^2A`

Prove the following identity :

`cosec^4A - cosec^2A = cot^4A + cot^2A`

Prove the following identity :

`sec^2A + cosec^2A = sec^2Acosec^2A`

Prove the following identity :

`cos^4A - sin^4A = 2cos^2A - 1`

Prove the following identity:

tan²A − sin²A = tan²A · sin²A

Prove the following identity :

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

Prove the following identity :

`(cosA + sinA)^2 + (cosA - sinA)^2 = 2`

Prove the following identity :

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

Prove the following identity :

`sec^2A.cosec^2A = tan^2A + cot^2A + 2`

Prove the following identity : 

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

Prove the following identity : 

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

Prove the following identity : 

`sin^4A + cos^4A = 1 - 2sin^2Acos^2A`

Prove the following identity : 

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