Trigonometrical Equations 1 Question 18
18. The equation $2 \cos ^{2} \frac{x}{2} \sin ^{2} x=x^{2}+x^{-2}, x \leq \frac{\pi}{9}$ has
(a) no real solution
(b) one real solution
(c) more than one real solution
(d) None of the above
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Answer:
Correct Answer: 18. (d)
Solution:
- Given equation is $2 \cos ^{2} \frac{x}{2} \sin ^{2} x=x^{2}+x^{-2}, x \leq \frac{\pi}{9}$
LHS $=2 \cos ^{2} \frac{x}{2} \sin ^{2} x<2$ and RHS $=x^{2}+\frac{1}{x^{2}} \geq 2$
$\therefore$ The equation has no real solution.
