मराठी

The Value of Cos − 1 ( Cos 5 π 3 ) + Sin − 1 ( Sin 5 π 3 ) is (A) π 2 (B) 5 π 3 (C) 10 π 3 (D) 0 - Mathematics

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प्रश्न

The value of \[\cos^{- 1} \left( \cos\frac{5\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{5\pi}{3} \right)\] is

 

पर्याय

  • `pi/2`

  • `(5pi)/3`

  • `(10pi)/3`

  • 0

MCQ
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उत्तर

(d) 0

We have
\[\cos^{- 1} \left( \cos\frac{5\pi}{3} \right) + \sin^{- 1} \left( \sin\frac{5\pi}{3} \right) = \cos^{- 1} \left\{ \cos\left( 2\pi - \frac{\pi}{3} \right) \right\} + \sin^{- 1} \left\{ \sin\left( 2\pi - \frac{\pi}{3} \right) \right\}\]
\[ = \cos^{- 1} \left\{ \cos\left( \frac{\pi}{3} \right) \right\} + \sin^{- 1} \left\{ - \sin\left( \frac{\pi}{3} \right) \right\}\]
\[ = \cos^{- 1} \left\{ \cos\left( \frac{\pi}{3} \right) \right\} - \sin^{- 1} \left\{ \sin\left( \frac{\pi}{3} \right) \right\}\]
\[ = \frac{\pi}{3} - \frac{\pi}{3}\]
\[ = 0\]

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पाठ 4: Inverse Trigonometric Functions - Exercise 4.16 [पृष्ठ १२१]

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आरडी शर्मा Mathematics [English] Class 12
पाठ 4 Inverse Trigonometric Functions
Exercise 4.16 | Q 20 | पृष्ठ १२१

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