Question

The number of solutions of the equation sin x = cos2 x in the interval (0, 10) is _____.

Answer 1

The correct answer is 4
The given equation is sin x = cos2 x
This can be stated as
sin2x + sinx-1 = 0
Use the quadratic formula
$sinx = \frac{-1+\sqrt5}{2} = +ve$
Only 4 roots
Consider the following graph :

Fig. Graph

Therefore , the number of solutions for this equation is 4 solutions.