Exams › SSC CGL (Prelims) › General

If $\csc\theta + \cot\theta = 3$, then $\csc\theta - \cot\theta =$ ?

1. 1/3
2. 2/3
3. 3
4. 1

Correct answer: 1/3

Solution

Using $(\csc\theta+\cot\theta)(\csc\theta-\cot\theta)=\csc^2\theta-\cot^2\theta=1$. Since $\csc\theta+\cot\theta=3$, we get $3(\csc\theta-\cot\theta)=1$, so the required value is $1/3$.

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