Question #f89e8

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Answer 1 · 2017-04-15T02:11:40

${cot}^{2} x - csc x = 1$ $cot^2x-cscx=1$

$\Rightarrow {csc}^{2} x - 1 - csc x - 1 = 0$ $=>csc^2x-1-cscx-1=0$

$\Rightarrow {csc}^{2} x - csc x - 2 = 0$ $=>csc^2x-cscx-2=0$

$\Rightarrow {csc}^{2} x - 2 csc x + csc x - 2 = 0$ $=>csc^2x-2cscx+cscx-2=0$

$\Rightarrow csc x (csc x - 2) + 1 (csc x - 2) = 0$ $=>cscx(cscx-2)+1(cscx-2)=0$

$\Rightarrow (csc x - 2) (csc x + 1) = 0$ $=>(cscx-2)(cscx+1)=0$

when $csc x - 2 = 0$ $cscx-2=0$

$\Rightarrow sin x = \frac{1}{2} = sin (\frac{π}{6})$ $=>sinx=1/2=sin(pi/6)$

$=>x=npi+(-1)^npi/6" where "n inZZ$

when $cscx+1=0$

$=>sinx=-1=sin(-pi/2)$

$=>x=npi-(-1)^npi/2" where "n inZZ$