Question

if cos theta + sin theta equal to root 2 cos theta then show that cos theta minus sin theta equal to root 2 Sin Theta

Answer 1

=cos theta + sin theta=√2cos theta
(square both sides)
=cos square theta + sin square theta + 2sin theta.cos theta=2cos square theta
=1 + 2sin theta.cos theta=2cos square theta
=2 sin square theta= cos square theta+cos square theta-1
=2 sin square theta= cos square theta- sin square theta
=2 sin square theta= (cos theta+sin theta)(cos theta-sin theta)
=2 sin square theta= √2cos theta (cos theta-sin theta)
=√2sin theta=cos theta - sin theta ( by solving)