# SOLUTION: Verify following is an identity. (1++sin(x))/sin(x)=(cot^2(x))/(csc(x)-1)

Algebra ->  Algebra  -> Trigonometry-basics -> SOLUTION: Verify following is an identity. (1++sin(x))/sin(x)=(cot^2(x))/(csc(x)-1)       Log On

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 Algebra: Trigonometry Solvers Lessons Answers archive Quiz In Depth

 Question 396589: Verify following is an identity. (1++sin(x))/sin(x)=(cot^2(x))/(csc(x)-1) Answer by lwsshak3(6505)   (Show Source): You can put this solution on YOUR website!Verify following is an identity. (1++sin(x))/sin(x)=(cot^2(x))/(csc(x)-1) Starting with the right hand side, notes: (cot^2(x))/(csc(x)-1) =(cos^2/sin^2)/((1/sin)-1) =(cos^2/sin^2)/(1-sin)/sin) =(cos^2/sin^2)*(sin/(1-sin)) (invert and multiply) =(cos^2/(sin)(1-sin) =(1-sin^2)/(sin)(1-sin) (difference of 2 squares) =(1+sin)(1-sin)/(sin)(1-sin) ((1-sin) cancels out) =(1+sin)/sin ans: right hand side=left hand side