Question

If cosΦ +sinΦ=√2cosΦ show that cosΦ-sinΦ=√2

Answer 1

hey mate :-


look this attachment :-


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Answer 2

(cosA+sinA)=√2cosA

Now squaring both side

(cosA+sinA)^2=(√2cosA)^2
cos^2A+sin^2A+2sinA.cosA=2cos^2A
cos^2A-sin^2A=2sinA.cosA

(cosA-sinA)^2=cos^2A+sin^2A-2sinA.cosA

(cosA-sinA)^2=cos^2A+sin^2A-cos^2A+sin^2A

(cosA-sinA)^2=2sin^2A
cosA-sinA=√2sinA