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Step-by-step explanation:
According to the Question:-
sin a + sin b = 2 sin( (a+b)/2 ) cos( (a-b)/2)
sin a - sin b = 2 sin( (a-b)/2 ) cos( (a+b)/2)
Right side:
Solving the Equation
cot x ( sin 5x - sin 3x) = cot x cdot 2 sin ( (5x-3x)/2) cos ( (5x+3x)/2)
= cos x / sin x cdot 2 sin x cos 4x = 2 cos x cos 4x
Left side:
Solving the Equation
cot(4x) ( sin 5x + sin 3x) =cot(4x) cdot 2 sin ( (5x+3x)/2) cos ( (5x-3x)/2)
= {cos 4x}/{sin 4x} cdot 2 sin 4x cos x = 2 cos x cos 4 x
HENCE PROVED,
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