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    Question

    which of the following is equal to [(tan θ +secθ -1)/

    (tanθ-secθ +1)]  
    A (4+sin θ)/cos θ Correct Answer Incorrect Answer
    B (1+cos θ)/sin θ Correct Answer Incorrect Answer
    C (1+sin θ)/cosecθ Correct Answer Incorrect Answer
    D (1+sin θ)/cos θ Correct Answer Incorrect Answer

    Solution

    [(tan θ +secθ -1)/ (tanθ-secθ +1)]         [sec2 θ- tan2 θ=1] = [ tan θ +secθ – (sec2 θ – tan2 θ)]/ (tan θ -sec θ+1) = (tan θ +sec θ) [(1-sec θ +tan θ)/ (tan θ-sec θ+1)] = tan θ +sec θ =sin θ / cos θ +1/cos θ = (1+sin θ)/cos θ

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