How do you prove # 1 + 1/(tan^2x) = 1/(sin^2x)#?

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How do you prove # 1 + 1/(tan^2x) = 1/(sin^2x)#?

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Answer 1 · 2015-12-12T11:57:47

I tried changing #tan# into #sin and cos#:

Explanation:

You can change the tangent as:
#tan(x)=sin(x)/cos(x)# and write it as:
#1+1/(sin^2(x)/cos^2(x))=1/sin^2(x)#
rearranging the left side:
#1+cos^2(x)/sin^2(x)=1/sin^2(x)#
#(sin^2(x)+cos^2(x))/sin^2(x)=1/sin^2(x)#
but: #sin^2(x)+cos^2(x)=1#
so:
#1/sin^2(x)=1/sin^2(x)#

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How do you prove # 1 + 1/(tan^2x) = 1/(sin^2x)#?

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