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

Question 207428: prove that sin^2 x ( 1 + cot^2 x ) = 1
THANK YOU!!
Answer by jim_thompson5910(35256) (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.
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