sin (pi/4 + x) sin (pi/4 - x) =1/2 cos 2x
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Step-by-step explanation:
RHS = sin (pi/4 + x) sin (pi/4 - x) = sin (π/4 + x) sin (π/4 - x)
= 2/2 sin (π/4 + x) sin (π/4 - x) = 2/2 sin (π/4 + x) cos (π/4+x)
= 2 sin (π/4 + x) cos (π/4+x) ÷ 2
= sin (π/2 + 2x) ÷ 2 = sin (π/2 - 2x) ÷ 2
= cos2x ÷ 2
= 1/2 cos 2x
= LHS
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