SOLUTION: Establish the identity Cos(a+B)/CosaSinB= Cot B - tan a

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Question 1150576: Establish the identity

Cos(a+B)/CosaSinB= Cot B - tan a
Answer by Edwin McCravy(20066) About Me  (Show Source):
You can put this solution on YOUR website!
cos%28A%2BB%29%2Fcos%28A%29sin%28B%29=cot%28B%29+-+tan%28A%29

Work with the left side

Use formula for cos(A+B)

%28cos%28A%29cos%28B%29-sin%28A%29sin%28B%29%29%2F%28cos%28A%29sin%28B%29%29

Break into two fractions:



Cancel cos(A)'s in the first fraction and sin(B)'s in second fraction:



%28cos%28B%29%29%2F%28sin%28B%29%29-%28sin%28A%29%29%2F%28cos%28A%29%29

Use quotient identities for cotangent and tangent:

cot%28B%29+-+tan%28A%29

Edwin