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Evaluate: (sin^2 30° + 4cot^2 45° – sec^2 60)(cosec^2 45° sec^2 30°)

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This is the basic and conceptual question from trigonometric ratios in which we have been asked to calculate the value of

(sin^2 30° + 4cot^2 45° – sec^2 60)(cosec^2 45° sec^2 30°)

RS Aggarwal, Class 10, chapter 11, question no 8

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  1. sin30=1/2

    sin^2 30=1/4

    cos45=1/√2=sin45

    cot45=1
    cot^2 45=1

    cos60=1/2
    sec60=2
    sec^2 60=4

    cos30=√3/2
    sec30=2/√3
    sec^2 30=4/3

    cosec45=1/sin45=√2
    cosec^2 45=2

    (sin^2 30+4cot45sec^2 60)(cosec^2 45sec^2 30)

    =[(1/2)^2+4×(1)^2(2)^2][(√2)^2×(2/√3)^2]

    =1/4×8/3

    =2/3.

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