SOLUTION: What is the simplified version of sinx + cosx • cotx

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Question 1081945: What is the simplified version of sinx + cosx • cotx
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28x%29%2Bcos%28x%29%2Acot%28x%29 Start with the given expression


sin%28x%29%2Bcos%28x%29%2A%28cos%28x%29%2Fsin%28x%29%29 Rewrite cotangent (cot) into cosine (cos) over sine (sin)


sin%28x%29%2B%28cos%28x%29%2F1%29%2A%28cos%28x%29%2Fsin%28x%29%29 Rewrite the fist cos%28x%29 term into cos%28x%29%2F1


sin%28x%29%2B%28cos%28x%29%2Acos%28x%29%29%2F%281%2Asin%28x%29%29 Multiply the fractions


sin%28x%29%2B%28cos%5E2%28x%29%29%2F%28sin%28x%29%29 Multiply


sin%28x%29%2A%281%29%2B%28cos%5E2%28x%29%29%2F%28sin%28x%29%29 Multiply the first sin%28x%29 term by (1)


sin%28x%29%2A%28sin%28x%29%2Fsin%28x%29%29%2B%28cos%5E2%28x%29%29%2F%28sin%28x%29%29 Rewrite the %281%29 into %28sin%28x%29%2Fsin%28x%29%29


Rewrite the fist sin%28x%29 term into sin%28x%29%2F1


Multiply the fractions


%28sin%5E2%28x%29%29%2F%28sin%28x%29%29%2B%28cos%5E2%28x%29%29%2F%28sin%28x%29%29 Multiply


%28sin%5E2%28x%29%2Bcos%5E2%28x%29%29%2F%28sin%28x%29%29 Add the fractions


%281%29%2F%28sin%28x%29%29 Use the pythagorean trig identity sin%5E2%28x%29%2Bcos%5E2%28x%29=1


csc%28x%29 Use the reciprocal trig identity %281%29%2F%28sin%28x%29%29=csc%28x%29


"csc" is shorthand for "cosecant"


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In the end, sin%28x%29%2Bcos%28x%29%2Acot%28x%29 simplifies to csc%28x%29


Note: Here is a list of trig identities and other trig reference material.