1.

If $ \cos \theta+\sin \theta=\sqrt{2} \cos \theta, $ show that$ \cos \theta-\sin \theta=\sqrt{2} \sin \theta $

Answer»

cosA+sinA=√2cosAsquaring both the sides =>(cosA+sinA)²=2cos²A=>cos²A+sin²A+2sinAcosA=2cos²A=>cos²A-2cos²A+2sinAcosA= -sin²A=> -cos²A+2sinAcosA= -sin²A=> cos²A-2sinAcosA=sin²Aadding sin²A on both the sides => cos²A+sin²A-2sinAcosA=2sin²A=> (cosA-sinA)²=2sin²A=> cosA-sinA=√2sinA



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