(English Medium) ICSE Class 9 - CISCE Question Bank Solutions

If θ = 30°, verify that: 1 - sin 2θ = (sinθ - cosθ)² 

Evaluate the following: `((sin3θ - 2sin4θ))/((cos3θ - 2cos4θ))` when 2θ = 30°

Evaluate the following: `((1 - cosθ)(1 + cosθ))/((1 - sinθ)(1 + sinθ)` if θ = 30°

If θ = 15°, find the value of: cos3θ - sin6θ + 3sin(5θ + 15°) - 2 tan²3θ

If A = B = 60°, verify that: cos(A - B) = cosA cosB + sinA sinB

If A = B = 60°, verify that: sin(A - B) = sinA cosB - cosA sinB

If A = B = 60°, verify that: tan(A - B) = `(tan"A" - tan"B")/(1 + tan"A" tan"B"")`

If θ < 90°, find the value of: sin²θ + cos²θ

If θ < 90°, find the value of: `tan^2θ - (1)/cos^2θ`

If `sqrt(3)`sec 2θ = 2 and θ< 90°, find the value of θ

If `sqrt(3)` sec 2θ = 2 and θ< 90°, find the value of

cos 3θ

If `sqrt(3)` sec 2θ = 2 and θ< 90°, find the value of

cos² (30° + θ) + sin² (45° - θ)

In the given figure, PQ = 6 cm, RQ = x cm and RP = 10 cm, find
a. cosθ
b. sin²θ- cos²θ
c. Use tanθ to find the value of RQ

Find the value of: `sqrt((1 - sin^2 60°)/(1 + sin^2 60°)` If 3 tan²θ - 1 = 0, find the value 
a. cosθ
b. sinθ

In a right triangle ABC, right angled at C, if ∠B = 60° and AB = 15units, find the remaining angles and sides.

If ΔABC is a right triangle such that ∠C = 90°, ∠A = 45° and BC =7units, find ∠B, AB and AC.

In a rectangle ABCD, AB = 20cm, ∠BAC = 60°, calculate side BC and diagonals AC and BD.

Find the value of 'x' in each of the following:

Find the value of 'x' in each of the following:

Find the value of 'x' in each of the following: