SOLUTION: Given that tan x = 8/15 and cos y = -(4/5) where x and y are in the same quadrant, calculate without using calculators, the value of tan (2x-45°).

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Question 1078868: Given that tan x = 8/15 and cos y = -(4/5) where x and y are in the same quadrant, calculate without using calculators, the value of tan (2x-45°).
Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
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Since "tan x = 8/15 and cos y = -(4/5) where x and y are in the same quadrant," it implies that "x" lies in QIII.


    (but this fact doesn't play any role in what follows. So this part of the condition is excessive and unnecessary) 


tan(2x) = %282%2Atan%28x%29%29%2F%281-tan%5E2%28x%29%29   (it is the formula for tan of double argument, one of the basic trigonometry formulas).


Therefore, tan(2x) = %282%2A%288%2F15%29%29%2F%281-%288%2F15%29%5E2%29 = %282%2A%288%2F15%29%29%2F%281-64%2F225%29 = %282%2A%288%2F15%29%29%2F%28%28225-64%29%2F225%29 = %282%2A8%2A225%29%2F%2815%2A161%29 = %282%2A8%2A15%29%2F161 = 240%2F161.


Next, tan(2x-45°) = %28tan%282x%29-tan%2845%5Eo%29%29%2F%281%2Btan%282x%29%2Atan%2845%5Eo%29%29   (from the difference formula for tangent)

= %28240%2F161-1%29%2F%281%2B%28240%2F161%29%2A1%29 = %28%28240-161%29%2F161%29%2F%28%28240%2B161%29%2F161%29 = %28240-161%29%2F%28240%2B161%29 = 79%2F401.

Answer. 79%2F401.