Chapter 3 Trigonometry – II Ex 3.4

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Chapter 3 Trigonometry – II Ex 3.4

Chapter 3 Trigonometry – II Ex 3.4

Question 1.
Express the following as a sum or difference of two trigonometric functions.
i. 2sin 4x cos 2x


iii. 2cos 4θ cos 2θ
iv. 2cos 35° cos 75°
Solution:

i. 2sin 4x cos 2x = sin(4x + 2x ) + sin (4x – 2x)
= sin 6x + sin 2x

ii.

iii. 2cos 4θ cos 2θ = cos(4θ + 2θ)+cos (4θ – 2θ)
= cos 6θ + cos 2θ

iv. 2cos 35° cos75°
= cos(35° + 75°) + cos (35° – 75°)
= cos 110° + cos (-40)°
= cos 110° + cos 40° … [∵ cos(-θ) = cos θ]

Question 2.
Prove the following:

Solution:

vi. sin 20° sin 40° sin 60° sin 80° = 3/16
Solution: