Question

If $y={\sec }^{-1}\left[cosecx\right]+cose{c}^{-1}\left[\sec x\right]+{\sin }^{-1}\left[\cos x\right]+{\cos }^{-1}\left[\sin x\right],$ then $\frac{dy}{dx}$ is equal to

• A. 0
• B. 2
• C. -2
• D. -4
• E. 1

Answer 1

Answer: (D)

$y=2{\cos }^{-1}\left(\sin x\right)+2{\sin }^{-1}\left(\cos x\right)$
$=2{\cos }^{-1}\cos \left(\frac{\pi }{2}-x\right)+2{\sin }^{-1}\sin \left(\frac{\pi }{2}-x\right)$
$=\pi -2x+\pi +2x=2\pi -4x$
$y^{\prime }=-4$