The value of cos-1- sin7-6 - is

Cos^ 1[ sin(7π6 ) ] = cos^ 1[cos(π2 + 7 π6 ) ] = cos^ 1[cos(10 π6 ) ] = cos^ 1[cos(5 π3 ) ] = cos^ 1[cos(2π π3 ) ] =cos^ 1[cosπ3] = π3 (∵cos^ 1(cos x)= ...

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Byju's Answer

Standard XII

Mathematics

Composition of Inverse Trigonometric Functions and Trigonometric Functions

The value of ...

Question

The value of ${cos}^{- 1} [- sin (\frac{7 π}{6})]$ is

\frac{5 π}{3}

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\frac{7 π}{6}

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\frac{π}{3}

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- \frac{7 π}{6}

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Solution

The correct option is C $\frac{π}{3}$
${cos}^{- 1} [- sin (\frac{7 π}{6})] = {cos}^{- 1} [cos (\frac{π}{2} + \frac{7 π}{6})] = {cos}^{- 1} [cos (\frac{10 π}{6})] = {cos}^{- 1} [cos (\frac{5 π}{3})] = {cos}^{- 1} [cos (2 π - \frac{π}{3})] = {cos}^{- 1} [cos \frac{π}{3}] = \frac{π}{3} (∵ {cos}^{- 1} (cos x) = x, x \in [0, π])$

Alternate solution
${cos}^{- 1} [- sin (\frac{7 π}{6})]$
$= {cos}^{- 1} [- sin (π + \frac{π}{6})]$
$= {cos}^{- 1} [sin (\frac{π}{6})]$
$= {cos}^{- 1} (\frac{1}{2})$
$= \frac{π}{3}, ∵ {cos}^{- 1} (x) \in [0, π]$

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Composition of Inverse Trigonometric Functions and Trigonometric Functions

Standard XII Mathematics

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The value of cos−1[−sin(7π6)] is

The value of ${cos}^{- 1} [- sin (\frac{7 π}{6})]$ is