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

Prove the following identities:

cosec⁴ A (1 – cos⁴ A) – 2 cot² A = 1

Prove the following identities:

(1 + tan A + sec A) (1 + cot A – cosec A) = 2

If sin A + cos A = p and sec A + cosec A = q, then prove that : q(p² – 1) = 2p.

If x = a cos θ and y = b cot θ, show that:

`a^2/x^2 - b^2/y^2 = 1` 

If sec A + tan A = p, show that:

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

If tan A = n tan B and sin A = m sin B, prove that `cos^2A = (m^2 - 1)/(n^2 - 1)`

If 2 sin A – 1 = 0, show that: sin 3A = 3 sin A – 4 sin³ A

If 4 cos² A – 3 = 0, show that: cos 3 A = 4 cos³ A – 3 cos A

Prove that:

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

Prove that:

`cot^2A/(cosecA - 1) - 1 = cosecA`

Prove that:

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

Prove that:

cos A (1 + cot A) + sin A (1 + tan A) = sec A + cosec A

Prove that:

`(sinA - cosA)(1 + tanA + cotA) = secA/(cosec^2A) - (cosecA)/(sec^2A)`

Prove that:

`sqrt(sec^2A + cosec^2A) = tanA + cotA`

Prove that:

(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A

Prove that:

(tan A + cot A) (cosec A – sin A) (sec A – cos A) = 1

Prove that

`cot^2A-cot^2B=(cos^2A-cos^2B)/(sin^2Asin^2B)=cosec^2A-cosec^2B`

Prove that:

(cosec A – sin A) (sec A – cos A) sec² A = tan A

Prove that: 
(cosec θ - sinθ )(secθ - cosθ ) ( tanθ +cot θ) =1

Simplify 

sin A `[[sinA   -cosA],["cos A"  " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`