Prove that

[Hint: Express L.H.S.

To prove:

As equation on RHS is a simplified expression, so we must opt Left side equation and simplify it further so that we can get

LHS = RHS.

And thus we will be able to prove it.

∵ LHS =

By seeing the expression we can think that the problem can be solved using transformation formula:

By transformation formula, we have:

2 cos A cos B = cos(A + B) + cos (A – B)

-2 sin A sin B = cos(A + B) - cos (A – B)

Or cos A – cos B =

But as LHS expression does not contain ‘2’ in its term. So we multiply and divide the expression by 2.

∴ LHS =

Applying transformation formula, we have –

LHS =

⇒ LHS =

⇒ LHS = {∵ cos (-x) = cos x}

⇒ LHS =

Again, applying the transformation formula:

⇒ LHS =

⇒ LHS =

∴ LHS = sin 4θ sin = RHS

Hence: