Prove that sin^4θ=3/8-(1/2)cos2θ+(1/8)cos4θ

Steps to prove sin^4θ=3/8-(1/2)cos2θ+(1/8)cos4θ

L.H.S

=sin^4θ

=(sin^2θ)^2

={(1-cos2θ)/2}^2

=(1/4)(1-cos2θ)^2

=(1/4)[(1)^2+cos^2(2θ)-2.1.cos2θ]

=(1/4){1-2cos2θ+(1+cos4θ)/2}

=1/4-2cos2θ/4+(1+cos4θ)/8

=1/4-2cos2θ/4+1/8+cos4θ/8

=(2+1-4cos2θ+cos4θ)/8

=3/8-(1/2)cos2θ+(1/8)cos4θ

=R.H.S

Hence sin^4θ=3/8-(1/2)cos2θ+(1/8)cos4θ is proved.

Detail Information:-

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