The largest positive solution of 1+sin4⁡x=cos2⁡3x in [−5π/2,5π/2], is

We have,

$\begin{aligned} 1 + \sin^{4} x = \cos^{2} 3 x \\ \Rightarrow \sin^{2} 3 x + \sin^{4} x = 0 \end{aligned}$

$\Rightarrow \sin 3 x = 0$ and $\sin 4 x = 0$

$\Rightarrow 3 x = 0, \pm π, \pm 2 π, \pm 3 π, \pm 4 π, \pm 5 π, \pm 6 π, \pm 7 π$

and,

$4 x = \pm n π, n = 0, 1, 2, \dots, 10 < 190 > x = 0, \pm π, \pm 2 π$

The largest positive value of $x$ is $2 π$

The largest positive solution of $1 + \sin^{4} x = \cos^{2} 3 x$ in $[- 5 π / 2, 5 π / 2]$ , is