The value of sin-1sin17-4-cos-1cos27-5-tan-1tan37-6 is

Let y=sin^ 1(sin(17π4))+cos^ 1(cos(27π5))+tan^ 1(tan(37π6)) Now, sin(17π4)=sin(4π+π4)=sinπ4 and cos(27π5)=cos(6π 3π5)=cos3π5 and tan(37π6)=tan(6π+π6)=tanπ6 ⇒ y ...

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Standard XII

Mathematics

Sin2A and Cos2A in Terms of tanA

The value of ...

Question

The value of ${sin}^{- 1} (sin (\frac{17 π}{4})) + {cos}^{- 1} (cos (\frac{27 π}{5})) + {tan}^{- 1} (tan (\frac{37 π}{6}))$ is

\frac{50 π}{51}

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\frac{61 π}{60}

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\frac{71 π}{70}

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\frac{41 π}{40}

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Solution

The correct option is B $\frac{61 π}{60}$
Let $y = {sin}^{- 1} (sin (\frac{17 π}{4})) + {cos}^{- 1} (cos (\frac{27 π}{5})) + {tan}^{- 1} (tan (\frac{37 π}{6}))$
Now, $sin (\frac{17 π}{4}) = sin (4 π + \frac{π}{4}) = sin \frac{π}{4}$ and
$cos (\frac{27 π}{5}) = cos (6 π - \frac{3 π}{5}) = cos \frac{3 π}{5}$ and
$tan (\frac{37 π}{6}) = tan (6 π + \frac{π}{6}) = tan \frac{π}{6}$

$\Rightarrow y = {sin}^{- 1} sin \frac{π}{4} + {cos}^{- 1} cos \frac{3 π}{5} + {tan}^{- 1} tan \frac{π}{6}$
$\Rightarrow y = \frac{π}{4} + \frac{3 π}{5} + \frac{π}{6} = \frac{61 π}{60}$

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Sin2A and Cos2A in Terms of tanA

Standard XII Mathematics

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The value of sin−1(sin(17π4))+cos−1(cos(27π5))+tan−1(tan(37π6)) is

The correct option is B 61π60Let y=sin−1(sin(17π4))+cos−1(cos(27π5))+tan−1(tan(37π6)) Now, sin(17π4)=sin(4π+π4)=sinπ4 and cos(27π5)=cos(6π−3π5)=cos3π5 and tan(37π6)=tan(6π+π6)=tanπ6 ⇒y=sin−1sinπ4+cos−1cos3π5+tan−1tanπ6 ⇒y=π4+3π5+π6=61π60

The value of ${sin}^{- 1} (sin (\frac{17 π}{4})) + {cos}^{- 1} (cos (\frac{27 π}{5})) + {tan}^{- 1} (tan (\frac{37 π}{6}))$ is