The equation "sin (x) + cos (x) = 0" has only one solution set "$x=\frac{3\pi }{4}+\pi n$".
Why it has not solution set "$x=\frac{7\pi }{4}+\pi n$"? Although it satisfy the equation.
Please help quickly.
[Math] sin (x) + cos (x) = 0. Why this equation has only one solution set
trigonometry
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Best Answer
The equation is equivalent to $$\tan x=-1$$ since the two functions $\cos$ and $\sin$ don't vanish together so we find $$x\equiv\frac{3\pi}4\mod \pi$$