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. (a)

Solution:

  1. 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.



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