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Math Help - Proving Trig Identities

  1. #1
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    Proving Trig Identities

    Prove each trig identity below.

    (1) cos(pi/2 + x) = -sin(x)

    (2) cos(A + B) + cos(A - B) = 2 cosA cos B
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  2. #2
    Moo
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    Quote Originally Posted by magentarita View Post
    Prove each trig identity below.

    (1) cos(pi/2 + x) = -sin(x)

    (2) cos(A + B) + cos(A - B) = 2 cosA cos B
    (1) -> use this formula :
    \cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b), and remember these two values :
    \cos \tfrac \pi 2=0 \text{ and } \sin \tfrac \pi 2=1


    (2) -> use the formula above and this formula :
    \cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b) (this is because cosine is an even function and sine an odd function)
    Then, add up \cos(a-b)+\cos(a+b)
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  3. #3
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    \cos{(A \pm B)} = \cos{A}\cos{B} \mp \sin{A}\sin{B}

    For both questions, prove the LHS. I want to see your attempt and people will point out any mistakes, if any.
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  4. #4
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    Tips...

    Quote Originally Posted by Moo View Post
    (1) -> use this formula :
    \cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b), and remember these two values :
    \cos \tfrac \pi 2=0 \text{ and } \sin \tfrac \pi 2=1


    (2) -> use the formula above and this formula :
    \cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b) (this is because cosine is an even function and sine an odd function)
    Then, add up \cos(a-b)+\cos(a+b)
    Thanks for the tips.
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