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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 x^{2} + y^{2} 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°