# maths

If cosA + sinA= root2 cosA
Show that cosA - sinA= root2 sinA

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1. cosA + sinA= √2*cosA
=> sinA = √2*cosA - cosA
=> sinA = (√2 - 1)cosA

cosA - sinA = cosA - (√2 - 1)cosA
= √2*[cosA(√2 - 1)]
= √2*sinA

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

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