The value of \(sin\left(sin^{-1}\frac{1}{2}+cos^{-1}\frac{1}{2}\right

1.	The value of \(sin\left(sin^{-1}\frac{1}{2}+cos^{-1}\frac{1}{2}\right)\)= ?A. 0 B. 1 C. -1 D. none of these
Answer» Correct Answer is 1 Now, let x = sin\(\left(sin^{-1}\frac{1}{2}+cos^{-1}\frac{1}{2}\right)\) \(\Rightarrow x=sin\left(\frac{\pi}{2}\right)\) \(\left(\because sin^{-1}\theta+cos^{-1}\theta=\frac{\pi}{2}\right)\) ⇒ x = 1 \(\left(\because sin\left(\frac{\pi}{2}\right)=1\right)\)

The value of \(sin\left(sin^{-1}\frac{1}{2}+cos^{-1}\frac{1}{2}\right)\)= ?A. 0 B. 1 C. -1 D. none of these

Answer»

Correct Answer is 1

Now, let x = sin\(\left(sin^{-1}\frac{1}{2}+cos^{-1}\frac{1}{2}\right)\)

\(\Rightarrow x=sin\left(\frac{\pi}{2}\right)\) \(\left(\because sin^{-1}\theta+cos^{-1}\theta=\frac{\pi}{2}\right)\)

⇒ x = 1 \(\left(\because sin\left(\frac{\pi}{2}\right)=1\right)\)