Question

if cos theta + sin theta = √2 sin theta show that​ cos theta - sin theta = √2sin theta​
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Answer 1

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...