The number of real solutions x of the equatio | vedclass

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Question

(b)

We have,

$\cos ^2(x \sin (2 x))+\frac{1}{1+x^2}=\cos ^2 x+\sec ^2 x$

$	ext { LHS }=\cos ^2(x \sin 2 x)+\frac{1}{1+x^2}$

$\cos ^2(x \s

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(b)

We have,

$\cos ^2(x \sin (2 x))+\frac{1}{1+x^2}=\cos ^2 x+\sec ^2 x$

$	ext { LHS }=\cos ^2(x \sin 2 x)+\frac{1}{1+x^2}$

$\cos ^2(x \sin 2 x)+\frac{1}{1+x^2} \leq 2$

$	ext { RHS }=\cos ^2 x+\sec ^2 x \geq 2$

$\qquad \quad \operatorname{LHS}^2 x+\sec ^2 x=2 	ext { at } x=0$

Hence, only one solution.

The number of real solutions $x$ of the equation $\cos ^2(x \sin (2 x))+\frac{1}{1+x^2}=\cos ^2 x+\sec ^2 x$ is

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