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  1. The value of
    1
    -
    1
    is
    cosecθ - cotθsinθ
    1. 1
    2. cot θ
    3. cosec θ
    4. tan θ
Correct Option: B

Expression

=
1
-
1
cosecθ - cotθsinθ

=
cosec²θ - cot²θ
- cosecθ = cosec θ + cotθ – cosecθ = cotθ
cosecθ - cotθ

[cosec²θ – cot²θ = 1 & 1/sinθ = cosecθ]
Method-2 :
1
=
1
1
-
cosθ
sinθ
sinθsinθ

=
sinθ
-
1
-
sin²θ - 1 + cosθ
=
1 - cos²θ - 1 + cosθ
1 - cosθsinθsinθ(1 - cosθ)sinθ(1 - cosθ)

=
cosθ(-cosθ + 1)
=
cosθ
= cotθ
sinθ(1 - cosθ)sinθ



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