SOLUTION: Tan^2(157.5) in degrees

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Question 1006779: Tan^2(157.5) in degrees
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
tan%5E2%28%22157.5%B0%22%29=tan%5E2%28%22315%B0%22%2F2%29

There are at least 6 well-known formulas for the tangent of 
half an angle.  Since 315° is a special angle, (a QIV angle
with a reference angle of 45°), we can use any of these:

tan%28theta%2F2%29%22%22=%22%22sin%28theta%29%2F%281%2Bcos%28theta%29%29

tan%28theta%2F2%29%22%22=%22%22tan%28theta%29%2F%281%2Bsec%28theta%29%29

tan%28theta%2F2%29%22%22=%22%221%2F%28csc%28theta%29%2Bcot%28theta%29%29

tan%28theta%2F2%29%22%22=%22%22%281%2Bcos%28theta%29%29%2Fsin%28theta%29

tan%28theta%2F2%29%22%22=%22%22%28sec%28theta%29-1%29%2Ftan%28theta%29%29

tan%28theta%2F2%29%22%22=%22%22csc%28theta%29-cot%28theta%29%29

The last one is the simplest as it has no denominator. The others
will require more complicated simplification, but will all end
up with the same expression:

tan%28%22315%B0%22%2F2%29%22%22=%22%22%22%22=%22%22csc%28%22315%B0%22%29-cot%28%22315%B0%22%29%29%22%22=%22%22-sqrt%282%29-%28-1%29%29%22%22=%22%221-sqrt%282%29

Edwin