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## Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 3 Trigonometry Ex 3.6

Question 1.

Express each of the following as a sum or difference

(i) sin 35° cos 28°

(ii) sin 4x cos 2x

(iii) 2 sin 10θ cos 2θ

(iv) cos 5θ cos 2θ

(v) sin 5θ sin 4θ.

Solution:

Question 2.

Express each of the following as a product

(i) sin 75° – sin 35°

(ii) cos 65° + cos 15°

(iii) sin 50° + sin 40°

(iv) cos 35° – cos 75°.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x).

Solution:

Question 8.

Solution:

Question 9.

Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x.

Solution:

LHS = 1 + cos 2x + cos 4x + cos 6x

= (1 + cos 6x) + (cos 2x + cos 4x)

= 2cos^{2} 3x + 2cos 3x cos x

= 2 cos 3x (cos 3x + cos x)

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.

Solution:

### Samacheer Kalvi 11th Maths Solutions Chapter 3 Trigonometry Ex 3.6 Additional Questions

Question 1.

Solution:

Let cos 20° cos 40° cos 60° cos 80° = x

Multiply by 2 sin 20° on both sides.

Question 2.

Solution:

Question 3.

Prove that sin 50° – sin 70° + cos 80° = 0.

Solution:

LHS = sin 50° – sin 70° + cos 80°

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Prove that tan 70° – tan 20° – 2 tan 40° = 4 tan 10°

Solution:

Question 9.

Solution:

Question 10.

Solution:

Multiplying numerator and denominator by 2, we have