Question:
\(\sin\!\big(\sin^{-1}\tfrac12\big)=\) ?
\(\sin\!\big(\sin^{-1}\tfrac12\big)=\) ?
Show Hint
For any \(x\in[-1,1]\), \(\sin(\sin^{-1}x)=x\).
Updated On: Oct 17, 2025
- \(1\)
- \(\tfrac12\)
- \(\tfrac{\sqrt3}{2}\)
- \(0\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
\(\sin^{-1}\) returns an angle whose sine is the input. Thus \(\theta=\sin^{-1}\tfrac12\) satisfies \(\sin\theta=\tfrac12\). Applying \(\sin\) undoes \(\sin^{-1}\):
\[
\sin(\sin^{-1}\tfrac12)=\tfrac12.
\]
Was this answer helpful?
0
0
Top Bihar Board XII Mathematics Questions
- \(\frac{d}{dx} \left(\sec^2 x - \tan^2 x\right)\)
- \(\frac{d}{dx} \left( e^{2x} + 2e^x \right)\)
- \(\frac{d}{dx} \left[ \lim_{x \to a} \frac{x^n + a^n}{x + a} \right] \)
- \(\frac{d}{dx} \left( \sin^{-1} 2x \right)\)
- \(\frac{d}{dx} \left[ (x+2)(x^2 - 2x + 4) \right] \)
View More Questions
Top Bihar Board XII Inverse Trigonometric Functions Questions
- \(\frac{d}{dx} \left( \sin^{-1} 2x \right)\)
- \(\frac{d}{dx} \left[ 2 \tan^{-1} x \right] \)
- \(\int \frac{4 \tan^{-1} x}{1 + x^2} \, dx \)
- What is \( \cos^{-1} x + \sec^{-1} 1 \)?
- Find \( \cot^{-1} \left( \tan \frac{\pi}{7} \right) \).
View More Questions
Top Bihar Board XII Questions
- Which metal was first used by humans?
- Where is the Harappan site called Shortughai located?
- Where has the evidence of dockyard been found from Indus Valley Civilization?
- Which is referred to as Meluhha in Mesopotamian texts?
- Where have miniature pots of faience probably used as perfume bottles been found?
View More Questions