SOLUTION: Simplify the trigonometric Expression: (SIN X + TAN X)/TAN X My book says the answer is: COT X + 1 Not sure what steps to take. Thank you

Algebra ->  Trigonometry-basics -> SOLUTION: Simplify the trigonometric Expression: (SIN X + TAN X)/TAN X My book says the answer is: COT X + 1 Not sure what steps to take. Thank you      Log On


   

Question 988712: Simplify the trigonometric Expression:
(SIN X + TAN X)/TAN X
My book says the answer is: COT X + 1
Not sure what steps to take.
Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The book is wrong unfortunately. The answer should be cos%28x%29+%2B+1. Here are the steps showing why


%28sin%28x%29+%2B+tan%28x%29%29%2F%28tan%28x%29%29


%28sin%28x%29%29%2F%28tan%28x%29%29+%2B+%28tan%28x%29%29%2F%28tan%28x%29%29


%28sin%28x%29%2F1%29%2F%28sin%28x%29%2Fcos%28x%29%29+%2B+1


%28sin%28x%29%2F1%29%2A%28cos%28x%29%2Fsin%28x%29%29+%2B+1


%28sin%28x%29%2Acos%28x%29%29%2F%281%2Asin%28x%29%29+%2B+1


%28cross%28sin%28x%29%29%2Acos%28x%29%29%2F%281%2Across%28sin%28x%29%29%29+%2B+1


cos%28x%29+%2B+1

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So again, %28sin%28x%29+%2B+tan%28x%29%29%2F%28tan%28x%29%29 simplifies to cos%28x%29+%2B+1