Samacheer Kalvi 9th Maths Solutions Chapter 6 Trigonometry Ex 6.5

You can Download Samacheer Kalvi 9th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

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°