**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° = 3/16Solution:**