Trigonometrical Equations Ques 11
- 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
Show Answer
Answer:
Correct Answer: 11.(a)
Solution:
Formula:
Domain and Range of Trigonometric Functions:
- 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.
BETA
