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    Question

    If (1+sinθ)/cosθ = x, then find the value of

    secθ
    A (x^2+ 1)/x Correct Answer Incorrect Answer
    B (x^2+ 1)/2x Correct Answer Incorrect Answer
    C (x^2- 1)/x Correct Answer Incorrect Answer
    D (x^2- 1)/2x Correct Answer Incorrect Answer

    Solution

    (1+sinθ)/cosθ = x sinθ/cosθ  + 1/cosθ = x tanθ + secθ =  x  ...........................(i) We know that sec²θ-tan²θ =  1  or (secθ-tanθ)(secθ+tanθ) = 1 or x(secθ-tanθ) = 1 or secθ-tanθ = 1/x  ----(2) Subtracting (1) from (2), we will get,  2secθ = x +1/x = (x2+1)/x secθ =    (x2+ 1)/2x

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