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Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Roots of Equation.

The number of roots of the equation \(x^2+sin^2{x}-1\) in the closed interval \([0,\frac{\pi}{2}]\) is

- 0
- 2
- 53361
- 5082

Equation

Roots

Algebra

But try the problem first...

Answer:2

Source

Suggested Reading

B.Stat Objective Problem 711

Challenges and Thrills of Pre-College Mathematics by University Press

First hint

\(x^2+sin^2{x}-1=0\)

\(\Rightarrow x^{2}=cos^{2}x\)

we draw two graphs \(y=x^{2} and y=cos^{2}x\)

where intersecting point gives solution now we look for intersecting points

Second Hint

we get two intersecting points

Final Step

so number of roots is 2.

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