Question 1202700
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{{{csc^2(x) = cot(x) + 1}}}


{{{1+cot^2(x) = cot(x) + 1}}} Use a <a href = "https://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf">trig identity</a>


{{{cot^2(x) = cot(x)}}} Subtract 1 from both sides. The "1"s cancel.


{{{cot^2(x) - cot(x) = 0}}} Subtract cot(x) from both sides


{{{cot(x)(cot(x) - 1) = 0}}} Factor


{{{cot(x)=0}}} or {{{cot(x) - 1 = 0}}} Set each piece equal to zero


{{{cot(x)=0}}} or {{{cot(x) = 1}}}


{{{tan(x) = 0}}} or {{{tan(x) = 1}}} Use another trig identity.


I'll let the student finish up.
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