(cosA+sinA)² + (cosA-sinA)² = 2
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It is proved below!!!
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Step-by-step explanation:
by formula ,( a+b)² = a²+ b²+2ab
therefore , (cos A + sinA)² = cos²A + sin²A + 2sinAcosA -- eq1
by formula , ( a-b)² = a²+ b²- 2ab
we get , cos²A + sin² A - sinAcosA --eq²
adding eq1 and eq2 we get,
cos²A + sin²A + cos²A + sin²A. ( cosAsinA - cosAsinA cancelled out )
we know that cos² A + sin²A = 1
therefore , 1+1= 2 = RHS
hence proved
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