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

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`

Prove the following identity : 

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

Prove the following identity :

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

Prove the following identity :

`(cotA + tanB)/(cotB + tanA) = cotAtanB`

Prove the following identity :

`1/(tanA + cotA) = sinAcosA`

Prove the following identity :

`tanA - cotA = (1 - 2cos^2A)/(sinAcosA)`

Prove the following Identities :

`(cosecA)/(cotA+tanA)=cosA`

Prove the following identity : 

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

Prove the following identity : 

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

Prove the following identity : 

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

Prove the following identity : 

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