SOLUTION: what is the solution for 2sine squared theta minus 1 over sine theta times cosine theta equals tangent theta minus cotangent theta

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Question 1056518: what is the solution for
2sine squared theta minus 1 over sine theta times cosine theta equals tangent theta minus cotangent theta

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!




Multiply through by sin%28theta%29cos%28theta%29%29

2sin%5E2%28theta%29sin%28theta%29cos%28theta%29-1=sin%5E2%28theta%29-cos%5E2%28theta%29

2sin%5E3%28theta%29cos%28theta%29-1=sin%5E2%28theta%29-cos%5E2%28theta%29

2sin%5E3%28theta%29cos%28theta%29-sin%5E2%28theta%29=1-cos%5E2%28theta%29

2sin%5E3%28theta%29cos%28theta%29-sin%5E2%28theta%29=sin%5E2%28theta%29

2sin%5E3%28theta%29cos%28theta%29-2sin%5E2%28theta%29=0

2sin%5E2%28theta%29%28sin%28theta%29cos%28theta%29-1%29=0

Use the zero factor property:

2sin%5E2%28theta%29=0;  sin%28theta%29cos%28theta%29-1=0

sin%5E2%28theta%29=0;   sin%28theta%29cos%28theta%29=1

sin%28theta%29=0;    
                         
theta=n%2Api, where n is any integer.

I think the second equation has no solution:

sin%28theta%29cos%28theta%29=1

Multiply both sides by 2

2sin%28theta%29cos%28theta%29=2

That is the expression for sin%282theta%29

sin%282theta%29=2

That can have no solution because the absolute
values of the sine is always 1 or less.

So the only solution is theta=n%2Api

Edwin