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

Prove that:

(sec A − tan A)² (1 + sin A) = (1 − sin A)

Prove that:

`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`

Prove that:

`tanA/(1 - cotA) + cotA/(1 - tanA) = secA  "cosec"  A + 1`

Prove that:

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

Prove that:

2 sin² A + cos⁴ A = 1 + sin⁴ A 

Prove that:

`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`

Prove that:

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

Prove that:

(1 + tan A . tan B)² + (tan A – tan B)² = sec² A sec² B

Prove that:

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

If x cos A + y sin A = m and x sin A – y cos A = n, then prove that : x² + y² = m² + n²

If m = a sec A + b tan A and n = a tan A + b sec A, then prove that : m² – n² = a² – b²

If x = r sin A cos B, y = r sin A sin B and z = r cos A, then prove that : x² + y² + z² = r²

If sin A + cos A = m and sec A + cosec A = n, show that : n (m² – 1) = 2 m

If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x² + y² + z² = r²

If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m² + n²) cos² B = n².

How much money will be required to buy 200, Rs. 25 shares at a premium of Rs. 2?

How much money will be required to buy 125, Rs. 30 shares at a discount of Rs. 3?

Show that : tan 10° tan 15° tan 75° tan 80° = 1

Show that : `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec A cosec A`

Show that : `sinAcosA - (sinAcos(90^circ - A)cosA)/sec(90^circ - A) - (cosAsin(90^circ - A)sinA)/(cosec(90^circ - A)) = 0`