Question

Prove that sin 4 theta +cos 4 theta =1-2 sin2 theta * cos 2 theta

Answer 1

Answer:

I hope it help you ☺️☺️☺️☺️☺️

Step-by-step explanation:

R.H.S

1-2sin2 teta*cos 2 teta

=(sin 2 teta + cos 2 teta)-2 sin 2 teta*cos 2 teta

=sin 2 teta (1-2cos2teta)+cos2 teta

=sin2teta (sin 2 teta+cos 2 teta-2 cos 2teta)+cos2 teta

=sin 2 teta (sin 2 teta- cos 2 teta)+cos 2 teta

=sin 4 teta sin 2 teta*cos 2 teta* cos 2 teta+cos 2 teta

=sin 4 teta+ cos 2 teta (1-sin2+teta)

=sin 4 teta (sin 2 teta+cos 2 teta-sin 2 teta)

=sin 4 teta+ cos 2 teta(+cos 2 teta)

=sin 4 teta

I hope it helps you ☺️☺️☺️