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

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

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

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

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

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

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

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

cos 3θ

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

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

cos2 (30° + θ) + sin2 (45° - θ)

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

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

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

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

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

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

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

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

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

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

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

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

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

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

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

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

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

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

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

Find the length of AD. Given: ∠ABC = 60°, ∠DBC = 45° and BC = 24 cm.

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

Find lengths of diagonals AC and BD. Given AB = 24 cm and ∠BAD = 60°.

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

In a trapezium ABCD, as shown, AB ‖ DC, AD = DC = BC = 24 cm and ∠A = 30°. Find: length of AB

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

Find the length of EC.

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

In the given figure, AB and EC are parallel to each other. Sides AD and BC are 1.5 cm each and are perpendicular to AB. Given that ∠AED = 45° and ∠ACD = 30°. Find:
a. AB
b. AC
c. AE

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined

In the given figure, ∠B = 60°, ∠C = 30°, AB = 8 cm and BC = 24 cm. Find:
a. BE
b. AC

[23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Chapter: [23] Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Concept: undefined >> undefined
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