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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