Question

Prove that Sin(π/4+x)sin(π/4-x)=1/2cos2x

Answer 1

we have sin(a+b)sin(a-b)
=sin²a-sin²b



A/Q;

Sin(pie/4+x+pie/4-x)sin(pie/4+x-pie/4+x)
sin(pie/2)sin2x

Answer 2

Step-by-step explanation:

Sin(π/4+x)sin(π/4-x)

=1/2(2Sin(π/4+x)sin(π/4-x))

=1/2*[cos(π/4-x-π/4-x)/2+cos(π/4-x+π/4+x)

=1/2[cos(-2x)+cos(π/4+π/4)]

=1/2 [cos2x+0]

=1/2 cos2x