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Math Help - [SOLVED] finding the value of α

  1. #1
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    [SOLVED] finding the value of α

    How do find the value of α in

    sec(2α+6)cos(5α+3)=1
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  2. #2
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    Quote Originally Posted by somanyquestions View Post
    How do find the value of α in

    sec(2α+6)cos(5α+3)=1
    Use the sum formula for cosine

    \sec{(2a + 6^\circ)}\cos{(5a + 3^\circ)} = 1

    \frac{\cos{(5a + 3^\circ)}}{\cos{(2a + 6^\circ)}} = 1

    \frac{\cos{5a}\cos{3^\circ} - \sin{5a}\sin{3^\circ}}{\cos{2a}\cos{6^\circ} - \sin{2a}\sin{6^\circ}} = 1.


    Can you go from here?
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  3. #3
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    hmm i don't know that rule..
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  4. #4
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    \cos{(\alpha \pm \beta)} = \cos{\alpha}\cos{\beta} \mp \sin{\alpha}\sin{\beta}.

    This is a standard identity.
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  5. #5
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    I don't know "sec", can you tell me...
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  6. #6
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    Actually I've thought of an easier way...

    You have

    \frac{\cos{(5a + 3^\circ)}}{\cos{(2a + 6^\circ)}} = 1

    \cos{(5a + 3^\circ)} = \cos{(2a + 6^\circ)}

    5a + 3^\circ = 2a + 6^\circ

    3a = 3^\circ

    a = 1^\circ.
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  7. #7
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    it doesn't say anything about this in my book and we didn't go over this in class. strange.
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  8. #8
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    \sec{\theta} = \frac{1}{\cos{\theta}}.
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  9. #9
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    oh, thank you
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  10. #10
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    Dear somanyquestions,

    sec(2a+6)^{o}cos(5a+3)^{o}=1

    \frac{\cos{(5a + 3)}^o}{\cos{(2a + 6)^o}} = 1

    cos(5a+3) = cos(2a+6)

    \frac{\pi(5a+3)}{180}=2n{\pi}{\pm}\frac{{\pi}(2a+6  )}{180} ; n\in{Z}

    By simplification you would get, a = \frac{(360n-9)}{7} or a = 120n+1

    Dear Prove It,

    Your answer is a particular solution. For example a = 121^o also satisfies the given trignometric equation.

    Hope this helps.
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