Question

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sin x - cos x=0​

Answer 1

 

$\displaystyle\bf\\sin\,x-cos\,x=0\\\\sin\,x=cos\,x\\\\\frac{sin\,x}{cos\,x} =1\\\\tg\,x=1\\\\x=arctg(1)+k\pi;~~~k\in Z\\\\\boxed{\bf x=\frac{\pi}{4}+k\pi;~~~k\in Z} \\\\k \in \{...,-2,-1,0,1,2,...\}$