If cos+sin=√2cos then prove that cos-sin=√2sin …

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Puja Sahoo? 6 years, 10 months ago
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Gaurav Seth 6 years, 10 months ago
Let θ = x
cos x + sin x = √2 cos x
squaring on both side, we get......
cos2x + sin2x + 2cosxsinx = 2cos2x
2sinxcosx = 2cos2x - cos2x - sin2x
2sinxcosx = cos2x - sin2x
2sinxcosx = (cosx+sinx) (cosx - sinx)
2sinxcosx = (root2 cosx) (cosx - sinx)
2sinxcosx/root2 cosx = cosx - sinx
√2 sinx = cosx - sinx
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