Question

If sinA + cosA = √2cos(90 - A) find the value of cot A​

Answer 1

Formula :- cos (90 - A) = sin A

I am using x instead of A.

$\sin(x) + \cos(x) = \sqrt{2} \cos(90 - x) \\ \\ \sin(x) + \cos(x) = \sqrt{2} \sin(x) \\ \\ \frac{ \sin(x) + \cos(x) }{ \sin(x) } = \sqrt{2} \\ \\ \frac{ \sin(x) }{ \sin(x) } + \frac{ \cos(x) }{ \sin(x) } = \sqrt{2} \\ \\ 1 + \cot(x) = \sqrt{2} \\ \\ \cot(x) = \sqrt{2} - 1$

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