What is the value of cosec≤ft(-73π/3) ?

Correct Answer is : −23-{2}{{3}}−32

Correct Answer is : −23-{2}{{3}}−32

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UPSC NDA 2 2022 Mathematics Solved Paper

Question : 46 of 120

Marks: +1, -0

\left(-\frac{73\pi}{3}\right)

Solution:

Concept:

The cosecant function has a period of

2\pi

and is an odd function.

Thus,

\csc(2n\pi + \theta) = \csc\theta

and

\csc(-\theta) = -\csc\theta

Explanation:

We need to evaluate

\csc\left(-\frac{73\pi}{3}\right)

First, reduce the angle using the period.

Add

24\pi

(which equals

\frac{72\pi}{3}

) because it is a multiple of

2\pi

\csc\left(-\frac{73\pi}{3} + 24\pi\right) = \csc\left(\frac{-73\pi + 72\pi}{3}\right) = \csc\left(-\frac{\pi}{3}\right)

Now apply the odd property:

\csc\left(-\frac{\pi}{3}\right) = -\csc\left(\frac{\pi}{3}\right)

We know

\csc\left(\frac{\pi}{3}\right) = \frac{2}{\sqrt{3}}

Therefore, the value is

-\frac{2}{\sqrt{3}}

Answer:

-\frac{2}{\sqrt{3}}

(Option B).

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