If tan thita = 1 upon root 7 , then cosec square thita – sec square thita upon cosec square thita + sec square

Question

If tan thita = 1 upon root 7 , then cosec square thita – sec square thita upon cosec square thita + sec square

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Madelyn 4 weeks 2021-08-16T18:17:09+00:00 1 Answer 0 views 0

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    2021-08-16T18:18:40+00:00

    Tan theta = opposite side/adjacent side

    tan theta=1/root 7

    Therefore,

    Opposite side=1 and Adjacent side= root 7

    By Pythogoras theorem

    Hypotenuse^2=Adjacent^2+Opposite^2

    Hypotenuse^2 = root 7^2 + 1^2

    Hypotenuse^2 = 7+1

    Hypotenuse = root 8

    Sin theta = Opposite/ Hypotenuse

    Sin theta = 1/root 8

    Therefore,

    cosec theta = root 8/1

    cos theta = Adjacent/Hypotenuse

    Cos theta = root 7/root 8

    Therfore,

    sec theta = root 8/ root 7

    Now,

    Cosec^2 theta – Sec^2 theta / Cosec^2 theta + Sec^2 theta

    Root 8^2/1^2 – Root8^2/root 7^2 / root 8^2/1^2 + root8^2/root 7^2

    8/1-8/7 / 8/1+8/7

    56-8/7 /56+8/7

    48/7 / 64/7

    48/7 *7/64

    48/64

    3/4

    The answer is 3/4.

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