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Thread: trig problem

  1. #1
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    trig problem

    hi ive been given this question and im not sure how to do it.

    1. a) Prove that cosec^4 x - cot^4 x = cosec^2 x + cot^2 x
    b) solve for 90 degrees< x < 180 degrees

    cosec^4 x - cot^4 x = 2 - cot x

    thanks
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  2. #2
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    Quote Originally Posted by brooksy View Post
    hi ive been given this question and im not sure how to do it.

    1. a) Prove that cosec^4 x - cot^4 x = cosec^2 x + cot^2 x
    b) solve for 90 degrees< x < 180 degrees

    cosec^4 x - cot^4 x = 2 - cot x

    thanks
    cosec^4x-cot^4x=(cosec^2x)^2-(cot^2x)^2
    =(cosec^2x+cot^2x)(cosec^2x-cot^2x)
    =(cosec^2x+cot^2x)
    {a^2-b^2=(a-b)(a+b) and cosec^2x-cot^2x=1}
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  3. #3
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    thanks

    thanks for that. does anyone know how to do part 2. cheers
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  4. #4
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    Quote Originally Posted by brooksy View Post
    hi ive been given this question and im not sure how to do it.

    b) solve for 90 degrees< x < 180 degrees

    cosec^4 x - cot^4 x = 2 - cot x

    thanks

    cosec^4x-cot^4x=2-cot x
    cosec^4x-(cosec^4x-1)=2-cot x
    1=2-cot x
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