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

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`

Prove the following identity : 

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

Prove the following identity : 

`sqrt(cosec^2q - 1) = "cosq  cosecq"`

Prove the following identities:

`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`

Prove the following identity : 

`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`

Prove the following identity : 

`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq

Prove the following identity : 

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

Prove the following identities:

`(sec"A"-1)/(sec"A"+1)=(sin"A"/(1+cos"A"))^2`

Prove the following identity : 

`sqrt((secq - 1)/(secq + 1)) + sqrt((secq + 1)/(secq - 1))` = 2 cosesq

Prove the following identity : 

`(secθ - tanθ)^2 = (1 - sinθ)/(1 + sinθ)`

Prove the following identity : 

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

Prove the following identity : 

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

Prove the following identity : 

`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2Acos^2B)`

Prove the following identity :

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

Prove the following identity  :

`(1 + cotA)^2 + (1 - cotA)^2 = 2cosec^2A`

Prove the following identity : 

`sec^4A - sec^2A = sin^2A/cos^4A`