Question

( sin^4x + cos^4x +sin2x -1)/(sinx-1) =0

Answer 1

\(\Leftrightarrow sin^4x+cos^4x+sin2x-1=0\)

\(\Leftrightarrow1-2\cdot sin^2x\cdot cos^2x+sin2x-1=0\)

\(\Leftrightarrow-2sin^2x\cdot cos^2x+sin2x=0\)

\(\Leftrightarrow-2\cdot sin^2x\cdot cos^2x+2\cdot sinx\cdot cosx=0\)

\(\Leftrightarrow sinx\cdot cosx\left(-2sinxcosx+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}sinx=0\\cosx=0\\sinxcosx=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}sinx=0\\cosx=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=k\Pi\\x=\dfrac{\Pi}{2}+k\Pi\end{matrix}\right.\)