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The number of solutions of the equation \mathrm{\sin x=\cos ^{2} x} in the interval \mathrm{(0,10)} is ___________

Option: 1

4


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{\sin x=\cos ^{2} x }\\

\mathrm{\Rightarrow \sin x=1-\sin ^{2} x} \\

\mathrm{\Rightarrow \sin ^{2} x+\sin x-1=0}

\mathrm{\Rightarrow \sin x=\frac{-1 \pm \sqrt{1+4}}{2}} \\

               \mathrm{=\frac{-1+\sqrt{5}}{2}, \frac{-1-\sqrt{5}}{2}} \\

\mathrm{\text { As only }-1 \leq \frac{-1+\sqrt{5}}{2} \leq 1 }\\

\mathrm{\therefore \quad \sin x=\frac{-1+\sqrt{5}}{2}}

So 4 solutions

Hence answer is 4

Posted by

Suraj Bhandari

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