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March 30, 2017

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Given that a^2+b^2=2 and that (a/b)= tan(45degee+x), find a and b in terms of sinx and cosx.

I don't know what i'm supposed to do, and i don't come to an answer! Help, thanks!

my workings:

tan(45+x)= (1+tanx)/(1-tanx)
a/b = (1+tanx)/(1-tanx)
a(1-tanx)=b(1+tanx)
i square both sides...
a^2(1-tanx)^2 = b^2(1+tanx)^2
a^2 + b^2 = 2
a^2 = 2 - b^2
substitute:
(2-b^2)(1-tanx)^2 = b^2(1+tanx)^2

I don't know if im on the right track, but i don't seem to come to an answer when i expand the whole equation!

  • Trigonometry - ,

    From:
    a(1-tanx)=b(1+tanx)
    multiply both sides by cos(x) to get
    a(cos(x)-sin(x))=b(cos(x)+sin(x))
    Now square and simplify. The product terms will cancel out after you substitute b²=(2-a²) to give you a in terms of sin(x) and cos(x).
    You can do similarly for b.

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