Solution of the inequality $\sin^{4}{\left( \frac{x}{3} \right) + \cos^{4}{\left( \frac{x}{3} \right) \frac{1}{2}},}$ is given by

Question

Solution of the inequality $\sin^{4}{\left( \frac{x}{3} \right) + \cos^{4}{\left( \frac{x}{3} \right) > \frac{1}{2}},}$ is given by

Dr. Abubacker · Accepted Answer

(c)
$\sin^{4}{\frac{x}{3} + \cos^{4}{\frac{x}{3} > \frac{1}{2}} \Rightarrow 1 - \frac{1}{2}\sin^{2}{\frac{2x}{3} > \frac{1}{2}}}$
$\Rightarrow \sin^{2}{\frac{2x}{3} < 1 \Rightarrow \frac{2x}{3} \in \left( R - (2n + 1)\frac{\pi}{2} \right)}$
$\Rightarrow x \in R - \left( \frac{3n\pi}{2} + \frac{3\pi}{4} \right);n \in I$

Q. Solution of the inequality $\sin^{4}{\left( \frac{x}{3} \right) + \cos^{4}{\left( \frac{x}{3} \right) > \frac{1}{2}},}$ is given by

Explanation

Reviewed by Dr. Abubacker

Want more practice?