The solution of the trigonometric equation are, [tex]x=\frac{\pi}{2},\frac{3\pi}{2}[/tex]
Trigonometric equation:
Given equation are,
[tex]cos(\frac{\pi}{4} -x)=\frac{\sqrt{2} }{2}sinx[/tex]
We know that, [tex]cos(A-B)=cosA cosB+sinAsinB[/tex]
[tex]cos(\frac{\pi}{4} -x)=\frac{\sqrt{2} }{2}sinx\\\\cos\frac{\pi}{4} *cosx+sin\frac{\pi}{4} *sinx=\frac{\sqrt{2} }{2}sinx\\\\\frac{\sqrt{2} }{2}cosx+\frac{\sqrt{2} }{2}sinx=\frac{\sqrt{2} }{2}sinx\\\\\frac{\sqrt{2} }{2}cosx=0\\\\cosx=0\\\\x=\frac{\pi}{2},\frac{3\pi}{2}[/tex]
Hence, The solution of the trigonometric equation are, [tex]x=\frac{\pi}{2},\frac{3\pi}{2}[/tex]
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