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

If 2 sin x° − 1 = 0 and x° is an acute angle; find:

1. sin x°
2. x° 
3. cos x° and tan x°.

If 4 cos² x° - 1 = 0 and 0 ∠ x° ∠ 90°,
find:(i) x°
(ii) sin² x° + cos² x°
(iii) `(1)/(cos^2xx°) – (tan^2 xx°)`

If 4 sin² θ – 1 = 0 and angle θ is less than 90°, find the value of θ and hence the value of cos² θ + tan² θ.

If sin 3A = 1 and 0 < A < 90^°, find sin A

If 2 cos 2A =  `sqrt3` and A is acute,
find:
(i) A 
(ii) sin 3A
(iii) sin² (75° - A) + cos² (45° +A)

If sin x + cos y = 1 and x = 30°, find the value of y

From the given figure,
find:
(i) cos x°
(ii) x°
(iii) `(1)/(tan^2 xx°) – (1)/(sin^2xx°)` 
(iv) Use tan x^o, to find the value of y.

Use the given figure to find:
(i) tan θ°
(ii)  θ°
(iii) sin²θ° - cos²θ°
(iv) Use sin θ° to find the value of x.

Find the magnitude of angle A, if 2 sin A cos A - cos A - 2 sin A + 1 = 0

Solve for x : 2 cos 3x - 1 = 0

If 4 cos² x = 3 and x is an acute angle;
find the value of :
(i) x 
(ii) cos² x + cot² x
(iii) cos 3x (iv) sin 2x

In ΔABC, ∠B = 90° , AB = y units, BC = `(sqrt3)` units, AC = 2 units and angle A = x°, find:

1. sin x°
2. x°
3. tan x° 
4. use cos x° to find the value of y.

If 2 cos (A + B) = 2 sin (A - B) = 1;
find the values of A and B.

State for any acute angle θ whether cos θ increases or decreases as θ increases.

State for any acute angle θ whether tan θ increases or decreases as θ decreases.

Solve the following equation for A, if 2cos2A = 1

Solve the following equation for A, if sec 2A = 2

Solve the following equations for A, if `sqrt3` tan A = 1

Solve the following equation for A, if tan 3 A = 1

Solve the following equation for A, if 2 sin 3 A = 1