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Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 6 Trigonometry Ex 6.5

Multiple Choice Questions :

Question 1.
If sin 30° = x and cos 60° = y, then x2 + y2 is
(1) $$\frac{1}{2}$$
(2) 0
(3) sin 90°
(4) cos 90°
Hint:

Solution:
(1) $$\frac{1}{2}$$

Question 2.
If tan θ = cot 37°, then the value of θ is
(1) 37°
(2) 53°
(3) 90°
(4) 1°
Hint:
tan θ = cot 37°
tan (90° – 37°) = cot 37°
θ = 90°- 37° = 53°
Solution:
(2) 53°

Question 3.
The value of tan 72° tan 18° is
(1) 0
(2) 1
(3) 18°
(4) 72°
Hint:

Solution:
(2) 1

Question 4.
The value of $$\frac{2 \tan 30^{\circ}}{1-\tan ^{2} 30^{\circ}}$$ is equal to
(1) cos 60°
(2) sin 60°
(3) tan 60°
(4) sin 30°
Hint:

Solution:
(3) tan 60°

Question 5.
If 2 sin 2θ = $$\sqrt{3}$$, then the value of θ is
(1) 90°
(2) 30°
(3) 45°
(4) 60°
Hint:

Solution:
(2) 30°

Question 6.
The value of 3 sin 70° sec 20° + 2 sin 49° sec 51° is
(1) 2
(2) 3
(3) 5
(4) 60°
Hint:

Solution:
(3) 5

Question 7.
The value of $$\frac{1-\tan ^{2} 45^{\circ}}{1+\tan ^{2} 45^{\circ}}$$ is
(1) 2
(2) 1
(3) 0
(4) $$\frac{1}{2}$$
Hint:

Solution:
(3) 0

Question 8.
The value of cosec (70° + θ) – sec(20° – θ) + tan (65° + θ) – cot(25° – θ) is
(1) 0
(2) 1
(3) 2
(4) 3
Hint: cosec (70° + θ) – sec (20° – θ) + tan (65° + θ) – cot (25° – θ)

Solution:
(1) 0

Question 9.
The value of tan 1°tan 2° tan 3° … tan 89° is
(1) 0
(2) 1
(3) 2
(4) $$\frac{\sqrt{3}}{2}$$
Hint: tan (90° – 89°) tan (90° – 88°) …tan (90° -46°) tan 45° tan 46°… tan 88 tan 89° = cot 89° cot 88°… cot 46° (1) tan 46°… tan 88° tan 89° = 1
Solution:
(2) 1

Question 10.
Given that sin α = $$\frac{1}{2}$$ and cos β = $$\frac{1}{2}$$ , then the value of α + β is
(1) 0°
(2) 90°
(3) 30°
(4) 60°
Hint:

Solution:
(2) 90°