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Thread: Trig Proof - Help Please

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    Cadet Heresy's Avatar
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    Trig Proof - Help Please

    Question:

    Given that 0 < x < Pi/4, prove that tan(Pi/4 + x) = cosx + sinx/cosx - sinx

    I got this problem for homework on the leadup to an exam coming up in 3 weeks - someone help please?

    P.S. Im sorry that I don't know how type Pi....

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    D:< fluffchuck's Avatar
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    Re: Trig Proof - Help Please

    tan(pi/4 + x)
    = (tan(pi/4) + tan(x))/(1 - tan(pi/4)tan(x)) (tan expansion formula)
    = (1 + tan(x))/(1 - tan(x))
    = (cos(x) + tan(x)cos(x))/(cos(x) - tan(x)cos(x)) (multiplying the top and bottom by cos(x))
    = (cos(x) + sin(x))/(cos(x) - sin(x))
    jathu123 and Heresy like this.
    HSC 2017
    Chemistry - Physics - English (Standard) - Maths Ext 1 - Maths Ext 2

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    Cadet Heresy's Avatar
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    Re: Trig Proof - Help Please

    Quote Originally Posted by fluffchuck View Post
    tan(pi/4 + x)
    = (tan(pi/4) + tan(x))/(1 - tan(pi/4)tan(x)) (tan expansion formula)
    = (1 + tan(x))/(1 - tan(x))
    = (cos(x) + tan(x)cos(x))/(cos(x) - tan(x)cos(x)) (multiplying the top and bottom by cos(x))
    = (cos(x) + sin(x))/(cos(x) - sin(x))
    Thank you so much!

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