SOLUTION: 2 + cos135 degrees divided by cos^2 240 degrees

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Question 625026: 2 + cos135 degrees divided by cos^2 240 degrees
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
2+%2B+cos%28135%29%2Fcos%5E2%28240%29

cos(135)
135 degrees terminates in the 2nd quadrant. So its reference angle is 180-135 = 45 degrees. 45 is a special angle so we should know that cos%2845%29+=+sqrt%282%29%2F2. And since cos is negative in the second quadrant, cos%28135%29+=+-sqrt%282%29%2F2

cos(240)
240 degrees terminates in the 3rd quadrant. So its reference angle is 240-180 = 60 degrees. 60 is a special angle so we should know that cos%2860%29+=+1%2F2. And since cos is negative in the third quadrant, cos%28240%29+=+-1%2F2

Substituting these values into our expression we get:
2+%2B+%28-sqrt%282%29%2F2%29%2F%28-1%2F2%29%5E2
Squaring the denominator we get:
2+%2B+%28-sqrt%282%29%2F2%29%2F%281%2F4%29
As usual, dividing by a fraction is the same as multiplying by its reciprocal:
2+%2B+%28-sqrt%282%29%2F2%29%2A%284%2F1%29
which simplifies to:
2+%2B+-2sqrt%282%29