We know `sin(sin^-1theta)=theta if - pi/2<=theta<=pi/2` We have `sin^-1(sin4)=sin^-1{sin(pi-4)}` = π - 4

`Sin^-1(Sin4)` - Mathematics

Question

$\sin^{- 1} (\sin 4)$

Solution

We know

$\sin (\sin^{- 1} θ) = θ if - \frac{π}{2} \leq θ \leq \frac{π}{2}$

We have

$\sin^{- 1} (\sin 4) = \sin^{- 1} {\sin (π - 4)}$

= π - 4

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Inverse Trigonometric Functions (Simplification and Examples)

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Q 1.08 Q 1.07 Q 1.09

Chapter 4: Inverse Trigonometric Functions - Exercise 4.07 [Page 42]

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RD Sharma Mathematics [English] Class 12

Chapter 4 Inverse Trigonometric Functions
Exercise 4.07 | Q 1.08 | Page 42

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${Sin}^{- 1} (Sin 4)$ - Mathematics

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