The value of sin-1sin36-7-cos-1sin39-7 is

Sin^ 1sin36π7 = sin^ 1sin(5π +π7) = π7 cos^ 1sin39π7 =π2 sin^ 1sin(6π 3 π7) =π2 ( 3 π7) =π2+ (3 π7)=13 π14 ∴ The value of the above expression is π7+13 ...

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Standard XIII

Mathematics

Properties Derived from Trigonometric Identities

The value of ...

Question

The value of ${sin}^{- 1} sin \frac{36 π}{7} + {cos}^{- 1} sin \frac{39 π}{7}$ is

\frac{4 π}{7}

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\frac{π}{7}

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\frac{11 π}{14}

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\frac{3 π}{14}

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Solution

The correct option is C $\frac{11 π}{14}$
${sin}^{- 1} sin \frac{36 π}{7} = {sin}^{- 1} sin (5 π + \frac{π}{7}) = - \frac{π}{7} {cos}^{- 1} sin \frac{39 π}{7} = \frac{π}{2} - {sin}^{- 1} sin (6 π - \frac{3 π}{7}) = \frac{π}{2} - (- \frac{3 π}{7}) = \frac{π}{2} + (\frac{3 π}{7}) = \frac{13 π}{14}$

$∴$ The value of the above expression is $- \frac{π}{7} + \frac{13 π}{14} = \frac{11 π}{14}$

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Properties Derived from Trigonometric Identities

Standard XIII Mathematics

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The value of sin−1sin36π7+cos−1sin39π7 is

The correct option is C 11π14sin−1sin36π7=sin−1sin(5π+π7)=−π7cos−1sin39π7=π2−sin−1sin(6π−3π7)=π2−(−3π7)=π2+(3π7)=13π14 ∴ The value of the above expression is −π7+13π14=11π14

The value of ${sin}^{- 1} sin \frac{36 π}{7} + {cos}^{- 1} sin \frac{39 π}{7}$ is