if cos theta + sin theta = √2 sin theta show that cos theta - sin theta = √2sin theta
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Answer:
cos theta + sin theta = √2cos theta
by squaring both sides.
(Cos theta + sin theta)square = (√2costheta) square
cos square theta + sin square theta + 2 cos theta sin theta = 2cos square theta
sin square theta + 2 cos theta sin theta= 2cos square theta- cos square theta
sin square theta = cos square theta- 2 cos theta sin theta
(Add sin square theta on both side )
sin square theta+ sin square theta= cos square theta + sin square theta - 2 cos theta sin theta
{(a-b) square = (a)square +(b)square -2ab}
2 sin square theta= (cos theta- sin theta) square
√2sinthetasquare = cos theta- sin theta
√2 sin theta = cos theta - sin theta
so, cos theta- sin theta= √2 sin theta
proved...
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