This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Trigonometric Ratios – 1”.

1. If sin (A + B) = \(\frac {\sqrt {3}}{2}\) and tan (A – B) = 1. What are the values of A and B?

a) 37, 54

b) 35.7, 40.7

c) 50, 10

d) 52.5, 7.5

View Answer

Explanation: The value of sin (A + B) = \(\frac {\sqrt {3}}{2}\) and sin 60° = \(\frac {\sqrt {3}}{2}\)

∴ A + B = 60 (1)

The value of tan (A – B) = 1 and tan 45° = 1

∴ A – B = 45 (2)

Adding equation (1) and (2)

A + B = 60

+ A – B = 45

– – – – – – – – – – – – –

2 A = 105

A = 52.5

∴ B = 7.5

2. If cos θ = \(\frac {3}{4}\) then value of cos 2θ is ___________

a) \(\frac {1}{6}\)

b) \(\frac {1}{4}\)

c) \(\frac {1}{8}\)

d) \(\frac {3}{8}\)

View Answer

Explanation: cos 2θ = 2cos θ

^{2}– 1

cos θ = \(\frac {3}{4}\)

cos 2θ = 2(\(\frac {3}{4}\))

^{2}– 1

= \(\frac {1}{8}\)

3. If sin A = \(\frac {8}{17}\), what will be the value of cos A sec A?

a) 2

b) -1

c) 1

d) 0

View Answer

Explanation: sin A = \(\frac {8}{17}\)

cos A sec A can be written as cosA × \(\frac {1}{secA}\) = 1

∴ cos A sec A = 1

4. The value of each of the trigonometric ratios of an angle depends on the size of the triangle and does not depend on the angle.

a) True

b) False

View Answer

Explanation:

Consider, two triangles ABC and DEF

In ∆ABC,

sin B = \(\frac {AC}{AB} = \frac {10}{20} = \frac {1}{2}\) i.e. B = 30°

Now, in ∆DEF,

sin F = \(\frac {DE}{DF} = \frac {20}{40} = \frac {1}{2}\) i.e. F = 30°

From these examples it is evident that the value of the trigonometric ratios depends on their angle and not on their lengths.

5. If tan α = √3 and cosec β = 1, then the value of α – β?

a) -30°

b) 30°

c) 90°

d) 60°

View Answer

Explanation: tan α = √3 and tan 60° = √3

∴ α = 60°

Cosec β = 1 and cosec 90° = 1

∴ β = 90°

α – β = 60 – 90 = -30°

6. In triangle ABC, right angled at C, then the value of cosec (A + B) is __________

a) 2

b) 0

c) 1

d) ∞

View Answer

Explanation:

Since the triangle is right angles at C,

The sum of the remaining two angles will be 90

∴ cosec(A + B) = Cosec 90° = 1

7. If tan θ = \(\frac {3}{4}\) then the value of sinθ is _________

a) \(\frac {3}{5}\)

b) \(\frac {4}{4}\)

c) \(\frac {3}{4}\)

d) \(\frac {-3}{5}\)

View Answer

Explanation:

tanθ = \(\frac {BC}{AC} = \frac {3}{4} = \frac {3k}{4k}\)

Hence, BC = 3k, AC = 4k

Using Pythagoras theorem

AB

^{2}= AC

^{2}+ BC

^{2}

AB

^{2}= 4k

^{2}+ 3k

^{2}

AB = 5k

sinθ = \(\frac {BC}{AB} = \frac {3k}{5k} = \frac {3}{5}\)

8. What is the value of sin30°cos15° + cos30°sin15°?

a) \(\frac {1}{2}\)

b) 0

c) 1

d) \(\frac {1}{\sqrt {2}}\)

View Answer

Explanation:

sin30°cos15° + cos30°sin15° = sin45° = \(\frac {1}{\sqrt {2}}\)

9. What is the value of cos A sec A + sin A cosec A – tan A cot A?

a) 0

b) 2

c) 1

d) 3

View Answer

Explanation:

Cos A sec A = 1

Similarly sin A cosec A = 1 and tan A cot A = 1

∴ cos A sec A + sin A cosec A – tan A cot A = 1 + 1 – 1 = 1

10. In a right angled triangle, the trigonometric function that is equal to the ratio of the side opposite a given angle to the hypotenuse is called cosine.

a) False

b) True

View Answer

Explanation:

In this ∆ ABC,

sin = \(\frac {Opposite}{hypotenuse}\)

**Sanfoundry Global Education & Learning Series – Mathematics – Class 10**.

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