If { ^{ - 1}}1/2 = { ^{ - 1}} x, then x =

Correct Answer is : 13{1}{{ 3 }}31

Correct Answer is : 13{1}{{ 3 }}31

Test Index

AP DSC School Assistant Math Model Test 3

Section: Subject Specific

Question : 105 of 160

Marks: +1, -0

{\sin ^{ - 1}}\frac{1}{2} = {\tan ^{ - 1}}

x, then x =

Solution:

Concept:

Use inverse trigonometric identities and known standard angle values.

Explanation:

We are given

\sin^{-1}\frac{1}{2} = \tan^{-1}x

. Recall that

\sin 30^\circ = \frac{1}{2}

, so

\sin^{-1}\frac{1}{2} = 30^\circ

(taking the principal value). Thus the equation becomes

30^\circ = \tan^{-1}x

. Taking

\tan

of both sides gives

\tan 30^\circ = x

. Since

\tan 30^\circ = \frac{1}{\sqrt{3}}

, we obtain

x = \frac{1}{\sqrt{3}}

Answer:

x = \frac{1}{\sqrt{3}}

; option B is correct.

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