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## Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 3 Trigonometry Ex 3.8

Question 1.

Find the principal solution and general solutions of the following:

Solution:

Question 2.

Solve the following equations for which solutions lies in the interval 0° < θ < 360°

(i) sin^{4} = sin^{2}x

(ii) 2 cos^{2} x + 1 = – 3cos x

(iii) 2 sin^{2} x + 1 = 3 sin x

(iv) cos 2x = 1 – 3 sin x – 3 sin x

Solution:

Question 3.

Solve the following equations:

(i) sin 5x – sin x = cos 3x

(ii) 2 cos^{2} θ + 3 sin θ – 3 = 0

(iii) cos θ + cos 3θ = 2 cos 2θ

(iv) sin θ + sin 3θ + sin 5θ = 0

(v) sin 2θ – cos 2θ – sin θ + cos θ = 0

(vi) sin θ + cos θ = \(\sqrt{3}\)

(vii) sin θ + \(\sqrt{3}\) cos θ = 1

(viii) cot θ + cosec θ = \(\sqrt{3}\)

Solution:

### Samacheer Kalvi 11th Maths Solutions Chapter 3 Trigonometry Ex 3.8 Additional Questions

Question 1.

Solve: 2 cos^{2} θ + 3 sin θ = 0

Solution:

2 cos^{2} θ + 3 sin θ = 0

⇒ 2 (1 – sin^{2} θ) + 3 sin θ = 0

⇒ 2 – 2 sin^{2} θ + 3 sin θ = 0

⇒ -2 sin^{2} θ + 3 sin θ + 2 = 0

⇒ 2 sin^{2} θ – 3 sin θ – 2 = 0

⇒ (2 sin θ + 1)(sin θ – 2) = 0

Question 2.

Solve: 2 tan θ – cot θ = -1

Solution:

2 tan θ – cot θ = -1

Question 3.

Solve: tan^{2} θ + (1 – \(\sqrt{3}\)) = 0

Solution:

Question 4.

Solve: \(\sqrt{3}\) x + cos x = 2

Solution:

Question 5.

Solution: