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

The given equation is sin x = cos2 xThis can be written as sin2x + sinx-1 = 0Use the quadratic formula sinx =−1+52=+veOnly 4 rootsConsider the graph

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

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answer is 4.

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The given equation is sin x = cos² x
This can be written as

sin²x + sinx-1 = 0

Use the quadratic formula

sinx $= \frac{- 1 + \sqrt{5}}{2} = + ve$

Only 4 roots

Consider the graph

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