Answer :
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:
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