The expression of θ+θ-1/θ+θ+1 is equal to

Correct Answer is : 1+cos⁡θsin⁡θ1+θ/θsinθ1+cosθ

Correct Answer is : 1+cos⁡θsin⁡θ1+θ/θsinθ1+cosθ

Test Index

SSC CGL Tier II 1 Dec 2016 Paper 1

Question : 95 of 100

Marks: +1, -0

\frac{\cot\theta+\csc\theta-1}{\cot\theta+\csc\theta+1}

is equal to

Solution:

(*)

\frac{\cot\theta+\csc\theta-1}{\cot\theta-\csc\theta+1}

(we have taken

(\cot\theta-\csc\theta+1)

instead of

(\cot\theta+\csc\theta+1)

as denominator)

= \frac{\cot\theta+\csc\theta - (\csc^2\theta - \cot^2\theta)}{\cot\theta-\csc\theta+1}

= \frac{\cot\theta+\csc\theta - (\csc\theta+\cot\theta)(\csc\theta-\cot\theta)}{\cot\theta-\csc\theta+1}

= \frac{(\cot\theta+\csc\theta) - (1-\csc\theta+\cot\theta)}{\cot\theta-\csc\theta+1}

= \cot\theta+\csc\theta

= \frac{\cos\theta}{\sin\theta} + \frac{1}{\sin\theta}

= \frac{\cos\theta+1}{\sin\theta}

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