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

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Answer 1 · 2015-04-19T22:29:40

Know that:

#cot^2x=1/tan^2x#

And also that:

#sin^2x+cos^2x=1#

#sin^2x/sin^2x+cos^2x/sin^2x=1/sin^2x#

#1+cot^2x=1/sin^2x#

Therefore:

#LHS#

#=1+1/tan^2x#

#=1+cot^2x#

#=1/sin^2x#

#=RHS#