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Math Help - Prove the Trig Identity

  1. #1
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    Prove the Trig Identity

    Prove the trig identity.

    tan 70 = 2tan50 + tan20
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  2. #2
    Senior Member euclid2's Avatar
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    Quote Originally Posted by magentarita View Post
    Prove the trig identity.

    tan 70 = 2tan50 + tan20
    2tan 50+tan 20=(tan 20+tan 50)+tan 50.....1
    tan(50+20)=tan50+tan20/1-tan20.tan50
    tan70(1-tan20.tan50)=tan50+tan20......2
    now by comparing 1&2 we have 2tan 50+tan 20=tan70(1-tan20.tan50)+tan50
    =tan70-tan20.tan50.tan70+tan50 as (tan70=cot20) we have
    tan70-tan50+tan50=tan70
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  3. #3
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    ok...

    Quote Originally Posted by euclid2 View Post
    2tan 50+tan 20=(tan 20+tan 50)+tan 50.....1
    tan(50+20)=tan50+tan20/1-tan20.tan50
    tan70(1-tan20.tan50)=tan50+tan20......2
    now by comparing 1&2 we have 2tan 50+tan 20=tan70(1-tan20.tan50)+tan50
    =tan70-tan20.tan50.tan70+tan50 as (tan70=cot20) we have
    tan70-tan50+tan50=tan70
    This is a tough one.
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