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if cot theta =7/8 , evaluate (1+sin^2theta)(1-sin^2theta)/(1+cost^2theta)(1+co-^2theta)

the answer should be 49/64 but i couldn't get that answer. can any one help?

  • maths -

    if cot theta =7/8 , evaluate (1+sin^2theta)(1-sin^2theta)/(1+cos^2theta)(1+cos-^2theta)

    the answer should be 49/64 but i couldn't get that answer. can any one help?

  • maths -

    if cotØ = 7/8, then tanØ = 8/7
    make a sketch of the corresponding right-angled triangle to find the hypotenuse to be √113

    so sinØ = 8/√113 and cosØ = 7/√113

    then (1+sin^2theta)(1-sin^2theta)/(1+cos^2theta)(1+cos-^2theta)
    = (1+64/113)(1-64/113)/(1+49/113)^2
    = (1 - 64^2/113^2)/(162/113)^2
    = (8673/113^2) / (26244/13^2)
    = 8673/2644
    ≠ 49/64

    check your typing of the expression, the end part of
    cos-^2theta makes no sense

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