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Math Help - Simplgying trig functions

  1. #1
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    Simplgying trig functions

    Simplify the following:


    (sin q + tan q) / (1 + sec q)
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  2. #2
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    Quote Originally Posted by Mr_Green View Post
    Simplify the following:


    (sin q + tan q) / (1 + sec q)
    Multiply numerator and denominator by,
    \cos x
    Thus,
    \frac{\sin x\cos x+\tan x \cos x}{\cos x+\sec x\cos x}
    But,
    \tan x\cos x=\frac{\sin x}{\cos x}\cdot \cos x=\sin x
    And,
    \sec x\cos x=1
    Thus,
    \frac{\sin x\cos x+\sin x}{\cos x+1}
    Factor,
    \frac{\sin x(\cos x+1)}{(\cos x+1)}=\sin x
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  3. #3
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    Hello, Mr_Green!

    Simplify: . \frac{\sin\theta + \tan\theta}{1 + \sec\theta}

    We have: . \frac{\sin\theta + \frac{\sin\theta}{\cos\theta}}{1 + \frac{1}{\cos\theta}}


    Multiply by \frac{\cos\theta}{\cos\theta}\!:\;\;\frac{\cos\the  ta}{\cos\theta}\cdot\frac{\sin\theta + \frac{\sin\theta}{\cos\theta}}{1 + \frac{1}{\cos\theta}} \;= \;\frac{\sin\theta\cos\theta + \sin\theta}{\cos\theta + 1}


    Factor: . \frac{\sin\theta(\cos\theta + 1)}{\cos\theta + 1} \;=\;\sin\theta

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