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how to simlify tan^2(x)+1/tan^2(x)=csc^2(x)?
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- ?Lv 67 years ago
tan²(x)+1/tan²(x)=csc²(x), changing everything to sin and cos,
sin²(x)/cos²(x) + cos²(x)/sin²(x)= 1/sin²(x), rearranging
sin²(x)/cos²(x) = (1 - cos²(x))/sin²(x)
= sin²(x)/sin²(x) since sin²(x)+cos²(x)=1
so
sin²(x)/cos²(x)=1, i.e
tan²(x)=1, therefore
tan(x)=±1
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