Which of the following is equal to {\sin\theta}/ {1- cosec \theta} + {cosec \theta}/ {1 -\sin\theta} ?

Correct Answer is : sinθ+cosecθ+1

\sin\theta – cosec\theta – 1

SSC CPO SI and ASI Model Paper 6

Question : 138 of 200

Marks: +1, -0

Which of the following is equal to

{sinθ}/ {1- cosec θ} + {cosec θ}/ {1 -sinθ} ?

Solution:

{sinθ}/{1- cosec θ}+ {cosec θ} /{1- sinθ}

={sinθ}/{1-1 {sinθ}}+1/{sinθ}/{ 1 -{sinθ}}

={sin^2 θ}/{sinθ -1}+ 1/{sinθ(1- sinθ)}

={sin^2 θ} /{sinθ -1}-1/{ sinθ(sinθ -1)}

={sin^3 θ- 1}/{sinθ(sinθ- 1)}

={(sinθ 1)(sin^2 θ sinθ 1)}/{sinθ(sinθ -1)}

= sinθ + cosecθ + 1

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