Để pt có nghiệm \(\Rightarrow cosx\ge0\)
Khi đó \(\Rightarrow\left(1+sinx\right)^4=cos^2x\)
\(\Rightarrow\left(1+sinx\right)^4=1-sin^2x\)
\(\Rightarrow\left(1+sinx\right)^4=\left(1+sinx\right)\left(1-sinx\right)\)
\(\Rightarrow\left[{}\begin{matrix}sinx+1=0\\\left(1+sinx\right)^3=1-sinx\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}sinx=-1\\sinx\left(sin^2x+3sinx+4\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}sinx=-1\\sinx=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}sinx=-1\\cosx=-1\left(loại\right)\\cosx=1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{2}+k2\pi\\x=k2\pi\end{matrix}\right.\)
