Question

please answer correct option
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Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Option (a) 0 is the answer

Step-by-step explanation:

Given :

$\mathrm{cosec^{-1}2 + sin^{-1}\bigg(-\dfrac{1}{2}\bigg)}$

To find :

The value of the given expression from the options :

(a) 0

(b) π/3

(c) π

(d) 2π/3

Solution :

$\longmapsto \mathrm{cosec^{-1}2 + sin^{-1}\bigg(-\dfrac{1}{2}\bigg)}$

We know that,

$\boxed{\mathrm{cosec^{-1}x = sin^{-1}\bigg(\dfrac{1}{x}\bigg)}}$

$\implies \mathrm{sin^{-1}\bigg(\dfrac{1}{2}\bigg) + sin^{-1}\bigg(-\dfrac{1}{2}\bigg)}$

We know that,

$\boxed{\mathrm{sin^{-1}(-x) = -sin^{-1}x \ ; \ x \in [-1,1]}}$

Here, 1/2 is in between -1 and 1, so

$\implies \mathrm{sin^{-1}\bigg(\dfrac{1}{2}\bigg) - sin^{-1}\bigg(\dfrac{1}{2}\bigg)}$

$\implies \mathrm{\cancel{sin^{-1}\bigg(\dfrac{1}{2}\bigg)} - \cancel{sin^{-1}\bigg(\dfrac{1}{2}\bigg)}}$

$\implies \underline{\underline{\Large{\textbf{0}}}}$

$\therefore \underline{\boxed{\mathbf{cosec^{-1}2 + sin^{-1}\bigg(-\dfrac{1}{2}\bigg) = 0}}}$

Thus, (a) 0 is the correct answer.

Hope it helps!!