SOLUTION: Verify that the equation is an identity: [(cotTheta - tanTheta)/(1 - tanTheta)] - (cotTheta) = 1 When I was solving this my answer led to [(1-tan/tan) * (1/1-tan)] which res

Question 602458: Verify that the equation is an identity:
[(cotTheta - tanTheta)/(1 - tanTheta)] - (cotTheta) = 1
When I was solving this my answer led to [(1-tan/tan) * (1/1-tan)] which resulted into 1/tan. Since cot = 1/tan then I had to subtract 1/tan with 1/tan, resulting in 0. So my answer is wrong since 0 =/= 1.
Please help me with this problem. Also if you can, please show the steps so I can will hopefully get it. I really don't understand this at all. Thank you so much in advance!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'm going to use 'x' in place of 'theta' (as it's easier/faster to type out)

(cot(x) - tan(x))/(1 - tan(x)) - cot(x) = 1

(1/tan(x) - tan(x))/(1 - tan(x)) - cot(x) = 1

( 1/tan(x) - (tan(x)*tan(x))/tan(x) )/(1 - tan(x)) - cot(x) = 1

( 1/tan(x) - (tan^2(x))/tan(x) )/(1 - tan(x)) - cot(x) = 1

( ( 1-tan^2(x))/tan(x) )/(1 - tan(x)) - cot(x) = 1

( ( 1-tan^2(x))/tan(x) )/((1 - tan(x))/1) - cot(x) = 1

( ( 1-tan^2(x))/tan(x) )*(1/(1 - tan(x))) - cot(x) = 1

( 1-tan^2(x) )/(tan(x)(1 - tan(x))) - cot(x) = 1

( (1 - tan(x))(1 + tan(x)) )/(tan(x)(1 - tan(x))) - cot(x) = 1

( 1 + tan(x) )/tan(x) - cot(x) = 1

1/tan(x) + tan(x)/tan(x) - cot(x) = 1

cot(x) + 1 - cot(x) = 1

(cot(x) - cot(x)) + 1 = 1

0 + 1 = 1

1 = 1

So we've shown that the identity is true.
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