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Math Help - Sometimes, trig identities irk me.

  1. #1
    Newbie Pyruvate's Avatar
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    Sometimes, trig identities irk me.

    Here are two that I cannot seem to prove. Any and all help is appreciated.

    \frac{\cos^2(x) - \sin^2(x)}{1-\tan^2(x)} = \cos^2(x)

    \sin(2t) - \tan(t) = \tan(t)\cos(2t)
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Pyruvate View Post
    Here are two that I cannot seem to prove. Any and all help is appreciated.

    \frac{\cos^2(x) - \sin^2(x)}{1-\tan^2(x)} = \cos^2(x)
    start with the LHS. write \tan^2 x as \frac {\sin^2 x}{\cos^2 x} and combine the fractions in the denominator. you should see the answer almost immediately.

    \sin(2t) - \tan(t) = \tan(t)\cos(2t)
    start with the LHS. write \sin 2t as 2 \sin t \cos t and \tan t as \frac {\sin t}{\cos t}. simplify. you should see what to do from there

    as you are seeing, it is very important to know your standard trig identities for these problems
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  3. #3
    Newbie Pyruvate's Avatar
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    Oh wow, that first one was pretty obvious. Thank you very much. Unfortunately, for the second problem, I'm getting 2\tan(t)\cos(2t) as an answer.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Pyruvate View Post
    Oh wow, that first one was pretty obvious. Thank you very much. Unfortunately, for the second problem, I'm getting 2\tan(t)\cos(2t) as an answer.
    that's strange. i got the right answer. check your work, make sure you are using the identities correctly
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  5. #5
    Newbie Pyruvate's Avatar
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    Well, the 2 originated in the problem from the double-angle identity. How did you get rid of it?
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Pyruvate View Post
    Well, the 2 originated in the problem from the double-angle identity. How did you get rid of it?
    i didn't get rid of it. i ended up using it in an identity. after simplifying, i could pull out a {\color{red}2} \cos^2 t - 1. that is where the cos(2t) came from. that red 2 is the same 2 that came from the sin(2t)
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  7. #7
    Newbie Pyruvate's Avatar
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    It appears that for an hour, I'd forgotten how to factor. Once again, I thank you for your help.
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