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Trigonometry> If sin(piecosx)=cos(piesinx)? find x? pls...

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

Abhishek , 7 Years ago

Grade 12

1 Answers

Sujit Kumar

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.

Last Activity: 7 Years ago

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