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Math Help - Verifying trig identities, picture included! thanks a lot!

  1. #1
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    Verifying trig identities, picture included! thanks a lot!



    Thanks a lot!

    Actually the third one i got, it was relatively easy. may i please have help with the others? thanks
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  2. #2
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    Quote Originally Posted by gobbajeezalus View Post


    Thanks a lot!

    Actually the third one i got, it was relatively easy. may i please have help with the others? thanks
    1. Multiplying the LHS by \frac{1+\sin{\theta}}{1+\sin{\theta}} gives:

    \frac{\cos{\theta}(1+\sin{\theta})}{1-\sin^2{\theta}}

    Recall that \sin^2{\theta} + \cos^2{\theta} = 1

    \frac{\cos{\theta}(1+\sin{\theta})}{\cos^2{\theta}  } = \frac{1+\sin{\theta}}{\cos{\theta}}

    Something similar can be done to the RHS.

    2. \cos{\theta}\cot{\theta}
    = \cos{\theta} \frac{\cos{\theta}}{\sin{\theta}} = \frac{\cos^2{\theta}}{\sin{\theta}} = \frac{1-\sin^2{\theta}}{\sin{\theta}}

    Now simply split and simplify, and you're done.

    3 is too easy. Recall that \tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}
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