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

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"]]`

Using the remainder theorem, find the remainders obtained when x³ + (kx + 8 )x + k is divided by x + 1 and x − 2. 

Hence, find k if the sum of the two remainders is 1.

Shekhar had a fixed deposit of Rs 24000 for 3 years . If he received interest at 10% p.a compounded annually, find the amount received by him at the time of maturity.

Prashant borrowe Rs. 35000 at 12% p.a. compounded semi-annually. Find the amount he needs to pay back at the end of `1 1/2` years

Amita wanted to start a business for which she needed Rs, 40000. She borrowed this from Dolly at 10% p.a compounded semi-annually. Find the extra amount that she needs to pay at the end of two years to clear her debt. 

Pradeep gave Rs.16000 to a friend for 1.5 years at 15% p.a. compounded semi-annually. Find the interest earned by him at the end of 1.5 years.