Question

Giải các phương trình :

a) \(1+\sin x-\cos x=0\)

b) \(\cos^4x+\sin^4x=1\)

Answer 1

a)\(\Leftrightarrow1+\sin x-\sqrt{1-\sin^2x}=0\)

\(\Leftrightarrow1+\sin^2x+2\sin x=1-\sin^2x\)

\(\Leftrightarrow\sin^2x+\sin x=0\)

\(\Rightarrow\left[{}\begin{matrix}\sin x=0\\\sin x=-1\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=k.\pi\left(k\in Z\right)\\x=-\frac{\pi}{2}+k.2\pi\left(k\in Z\right)\end{matrix}\right.\)

Vậy...

b)\(\Leftrightarrow\cos^2x-\sin^2x=1\)

\(\Leftrightarrow\cos^2x-\left(1-\cos^2x\right)=1\)

\(\Leftrightarrow\cos^2x=1\)

\(\Rightarrow\left[{}\begin{matrix}x=k.2\pi\\x=\pi+k.2\pi\end{matrix}\right.\)

Vậy ....

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