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  • The value of the expression 2 sec inverse 2 plus sin inverse into bracket 1 divided 2 is A. pi divided 6 B. 5pi divided 6 C. 7pi divided 6 D.1

The value of the expression 2 \sec^{-1}2+\sin^{-1}\left ( \frac{1}{2} \right ) is

A.\frac{\pi}{6}

B.\frac{5\pi}{6}

C.\frac{7\pi}{6}

D.1

Answers (1)

Answer :(B)

We have,

Principal value of sin-1 x is  \left ( -\frac{\pi}{2},\frac{\pi}{2} \right )

Principal value of sec-1 x is [0, π]-\left \{ \frac{\pi}{2} \right \}

Let  \sin^{-1}\frac{1}{2}=A

\Rightarrow \sin A =\frac{1}{2}

\Rightarrow A =\frac{\pi}{6}

So, \Rightarrow \sin^{-1}\frac{1}{2}=\frac{\pi}{6}   … (1)


Let sec-1 2 = B

⇒ sec B = 2

\Rightarrow B=\frac{\pi}{3}

So, 2 sec-1 2 = 2B

\Rightarrow 2\sec^{-1}2=\frac{2\pi}{3}...(2)

So, the value of 2\sec^{-1}2+\sin^{-1}\frac{1}{2}  from (1) and (2) is

2\sec^{-1}2+\sin^{-1}\frac{1}{2}=\frac{2\pi}{3}+\frac{\pi}{6}

=\frac{4\pi}{6}+\frac{\pi}{6}

=\frac{5\pi}{6}

So, 2\sec^{-1}2+\sin^{-1}\frac{1}{2}=\frac{5\pi}{6}

Posted by

infoexpert24

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