Prove that cos θ cos θ/2 – cos 3θ cos 9θ/2 = sin7θ sin4θ [Hint: Express L.H.S. = ½ [2cos θcos θ/2 – 2cos 3θ cos 9θ / 2]

Solution:

By applying transformation formula, we have,

Now multiply and divide the expression by 2 .

Now using the transformation formula, we have,

As a result,