SOLUTION: Find exact value of tan(arcsec 17÷15 - cot -3÷4)

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Question 757595: Find exact value of tan(arcsec 17÷15 - cot -3÷4)
Answer by lwsshak3(11628) About Me  (Show Source):
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Find exact value of tan(arcsec 17÷15 - cot -3÷4)
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let sec(x)=17/15
Identity: tan%5E2%28x%29=sec%5E2%28x%29-1

tan(x)=8/15
..
let cot(y)=-3/4
tan(y)=-4/3
..
tan(arcsec 17÷15 - cot -3÷4)=tan(x-y)
Identity: tan%28x-y%29=%28tan%28x%29-tan%28y%29%29%2F%281%2Btan%28x%29tan%28y%29%29

%28%2828%2F15%29%29%2F%281-%2832%2F45%29%29=%2828%2F15%29%2F%2813%2F45%29=84/13
tan(arcsec 17÷15 - cot -3÷4)=84/13
..
calculator check:
cos(x)=15/17
x≈28.07º
tan(y)=-4/3
y≈126.87º (in Q2 where tan<0)
x-y=28.07-126.87≈-98.8º (in Q3 where tan>0)
tan(x-y)=tan(-98.8º)≈6.46
exact value=84/13≈6.46