Question #c0ad9

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Answer 1 · 2017-08-19T12:03:11

$1 + 2 csc x = cot x + 3 csc x$ $1+2cscx=cotx+3cscx$

$\Rightarrow sin x (1 + \frac{2}{sin x}) = sin x (\frac{cos x}{sin x} + \frac{3}{sin x})$ $=>sinx( 1+2/sinx)=sinx(cosx/sinx+3/sinx)$

$\Rightarrow sin x + 2 = cos x + 3$ $=>sinx+2=cosx+3$

$\Rightarrow \frac{1}{\sqrt{2}} sin x - \frac{1}{\sqrt{2}} cos x = \frac{1}{\sqrt{2}}$ $=>1/sqrt2sinx-1/sqrt2cosx=1/sqrt2$

$\Rightarrow cos (\frac{π}{4}) sin x - sin (\frac{π}{4}) cos x = sin (\frac{π}{4})$ $=>cos(pi/4)sinx-sin(pi/4)cosx=sin(pi/4)$

$\Rightarrow sin (x - \frac{π}{4}) = sin (\frac{π}{4})$ $=>sin(x-pi/4)=sin(pi/4)$

$=>x-pi/4=npi+(-1)^npi/4" where " nin ZZ$

$=>x=npi+(-1)^npi/4+pi/4" where " nin ZZ$