SOLUTION: prove that sin^2 x ( 1 + cot^2 x ) = 1 THANK YOU!!

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Question 207428: prove that sin^2 x ( 1 + cot^2 x ) = 1
THANK YOU!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sin^2 x ( 1 + cot^2 x ) = 1 ... Start with the given equation.


sin^2 x * 1 + sin^2 x * cot^2 x = 1 ... Distribute


sin^2 x * 1 + sin^2 x * (cos^2 x)/(sin^2 x) = 1 ... Replace cotangent with cosine over sine


sin^2 x + cos^2 x = 1 ... Multiply


1 = 1 ... Use the identity sin^2 x + cos^2 x = 1 to replace the left side


So this verifies the identity.