KVPY SX SB Exam 2018 Question Paper

Question : 6 of 120

Marks: +1, -0

The number of real solutions x of the equation

\cos^2(x \sin(2x)) + 1/{1+x^2}

= \cos^2x + \sec^2x

Solution:

\cos^ 2 (x \sin(2x)) + 1/{1+x^2}

= \cos^ 2 x + \sec^2 x

(which is ≥ 2)
But

0 ≤ \cos^2(x\sin x) ≤

\and 0 < 1/{1+x^2} ≤ 1

⇒ only one solution at x = 0, when every term becomes 1

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