How do you solve $csc x {cot}^{2} x = csc x$ $cscxcot^2x=cscx$ for $0 \leq x \leq 2 π$ $0<=x<=2pi$ ?

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Answer 1 · 2017-07-17T18:24:48

The Soln. Set $= {\frac{π}{4}, 3 \frac{π}{4}, 5 \frac{π}{4}, 7 \frac{π}{4}} \subset [0, 2 π] .$ $={pi/4,3pi/4,5pi/4,7pi/4} sub [0,2pi].$

$csc x {cot}^{2} x = csc x \Rightarrow csc x {cot}^{2} x - csc x = 0 .$ $cscxcot^2x=cscx rArr cscxcot^2x-cscx=0.$

$:. cscx(cot^2x-1)=0.$

Since, $AA x, csc x ne0, cot^2x=1 rArr cotx=+-1.$

$cotx=1 rArr x=pi/4, pi+pi/4=5pi/4.$

$cotx=-1 rArr x=pi-pi/4=3pi/4, 2pi-pi/4=7pi/4.$

Hence, the Soln. Set $={pi/4,3pi/4,5pi/4,7pi/4} sub [0,2pi].$

How do you solve cscxcot^2x=cscxcscxcot2x=cscxcscxcot^2x=cscx for 0<=x<=2pi0≤x≤2π0<=x<=2pi?