The number of solutions of the equation sin x = cos 2 x in the interval 0 , 10 is ______.

Question

The number of solutions of the equation sin x = cos 2 x in the interval 0 , 10 is ______.,

MARKS App · Accepted Answer

Given, sin x = cos 2 x ⇒ sin x = 1 - sin 2 x ⇒ sin 2 x + sin x - 1 = 0 ⇒ sin x = - 1 ± 5 2 ⇒ sin x = 5 - 1 2 Now plotting the graph we get, ⇒ Now by graph number of solutions in 0 , 10 = 4

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