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If sin(piecosx)=cos(piesinx)? Find x? please

If sin(piecosx)=cos(piesinx)? Find x? please

Grade:12

1 Answers

Sujit Kumar
111 Points
3 years ago
My solution to this question is given bellow.
sin(\pi cosx)=cos(\pi sinx)
\rightarrow sin(\pi cosx)=sin(\frac{\pi}{2} - \pi sinx)
\rightarrow \pi cosx=\frac{\pi}{2} - \pi sinx
\rightarrow cosx=\frac{1}{2} - sinx
\rightarrow sinx=\frac{1}{2} - (1-sin^{2}x)^{\frac{1}{2}}
\rightarrow (1-sin^{2}x)^{\frac{1}{2}}=\frac{1}{2} - sinx
SQUARING ON BOTH SIDES
\rightarrow (1-sin^{2}x)=\frac{1}{4} - sinx + sin^{2}x
\rightarrow 2sin^{2}x - sinx-\frac{3}{4}=0
\rightarrow 8sin^{2}x - 4sinx-3=0
SOLVING THE QUADRATIC EQUATION
\rightarrow sinx=\frac{4\pm (16+96)^{\frac{1}{2}}}{16}
\rightarrow sinx=\frac{1\pm (7)^{\frac{1}{2}}}{4}
\rightarrow x=sin^{-1}(\frac{1\pm (7)^{\frac{1}{2}}}{4})
This is the value of x according to me.

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