How do you solve sinx + cosx = 1?

sin x + cos x =1

Solution

sin x + cos x =1

On squaring both sides we get

\(\left ( sin x + cos x \right )^{2}= (1)^{2}\) \(\left ( sin^{2}x + cos^{2}x + 2sin x cos x \right )= 1\) \(\left ( 1 + 2sin x cos x \right )= 1\) \(\left (2sin x cos x \right )= 0\) \((2sin x cos x)= sin 2x\) \(sin 2x=0\) \(2x= 0,\pi\) \(x=2\pi n,\frac{\pi }{2}+2\pi n\) where n is an integer

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