The value of x in \(\big ( 0, \frac{π}{2}\big)\) satisfying the e

1.	The value of x in \(\big ( 0, \frac{π}{2}\big)\) satisfying the equation sin x cos x = \(\frac{1}{4}\) is(a) \(\frac{\pi}{6}\)(b) \(\frac{\pi}{8}\)(c) \(\frac{\pi}{12}\)(d) \(\frac{\pi}{4}\)
Answer» Answer : (c) \(\frac{π}{12}\) sin x cos x = \(\frac{1}{4}\) ⇒ 2 sin x cos x = \(\frac{1}{2}\) ⇒ sin 2x = \(\frac{1}{2}\) ⇒ sin 2x = sin \(\frac{π}{6}\) ⇒ 2x = \(\frac{π}{6}\) , x ∈ ( 0 , \(\frac{π}{2}\) ) ⇒ x = \(\frac{π}{12}\)

The value of x in \(\big ( 0, \frac{π}{2}\big)\) satisfying the equation sin x cos x = \(\frac{1}{4}\) is(a) \(\frac{\pi}{6}\)(b) \(\frac{\pi}{8}\)(c) \(\frac{\pi}{12}\)(d) \(\frac{\pi}{4}\)

Answer»

Answer : (c) \(\frac{π}{12}\)

sin x cos x = \(\frac{1}{4}\)

⇒ 2 sin x cos x = \(\frac{1}{2}\) ⇒ sin 2x = \(\frac{1}{2}\)

⇒ sin 2x = sin \(\frac{π}{6}\)

⇒ 2x = \(\frac{π}{6}\) , x ∈ ( 0 , \(\frac{π}{2}\) )

⇒ x = \(\frac{π}{12}\)