# Mathematics Questions and Answers – Trigonometric Ratios – 1

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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

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)
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) $$\frac {3}{8}$$

Explanation: cos 2θ = 2cos θ2 – 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

Explanation: sin A = $$\frac {8}{17}$$
cos A sec A can be written as cos⁡A × $$\frac {1}{sec⁡A}$$ = 1
∴ cos A sec A = 1
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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

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°

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) ∞

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) $$\frac {-3}{5}$$

Explanation: tanθ = $$\frac {BC}{AC} = \frac {3}{4} = \frac {3k}{4k}$$
Hence, BC = 3k, AC = 4k
Using Pythagoras theorem
AB2 = AC2 + BC2
AB2 = 4k2 + 3k2
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) $$\frac {1}{\sqrt {2}}$$

Explanation:
sin30°cos15° + cos30°sin15° = sin⁡45° = $$\frac {1}{\sqrt {2}}$$

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

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

Explanation: In this ∆ ABC,
sin = $$\frac {Opposite}{hypotenuse}$$

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