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  1. The expression of
    cotθ + cosecθ - 1
    is equal to
    cotθ - cosecθ + 1

    1. 1 + cosθ
      sinθ

    2. 1 - cosθ
      sinθ

    3. cotθ + 1
      cosecθ

    4. cotθ - 1
      cosecθ
    5. None of these
Correct Option: E

Expression =
cotθ + cosecθ - 1
cotθ - cosecθ + 1

we have taken (cot θ – cosec θ + 1) instead of (cot θ + cosec θ + 1) as denominator
Expression =
cotθ + cosecθ - (cosec2θ - cot2θ)
cotθ - cosecθ + 1

Expression =
(cotθ + cosecθ) - (cosecθ + cotθ)(cosecθ - cotθ)
cotθ - cosecθ + 1

Expression =
(cotθ + cosecθ)[ 1 - cosecθ + cotθ]
cotθ - cosecθ + 1

Expression = cotθ + cosecθ
Expression =
cosθ
+
1
sinθsinθ

Expression =
cosθ + 1
sinθ



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