The solutions of the equation |(1+sin^2x, sin^2x, sin^x), (cos^x, 1+cos^2x, cos^2x),(4sin2x,4sin2x,1 +4 sin2x)|= 0,(0 < x < π),

Question

The solutions of the equation

\(\begin{vmatrix}1+sin^2x&sin^2x&sin^2x\\cos^2x&1+cos^2x&cos^2x\\4sin2x&4sin2x&1+4sin2x\end{vmatrix}\) = 0,

(0 < x π), are

(1) \(\frac{\pi}{12},\frac{\pi}6\) 

(2) \(\frac{\pi}{6},\frac{5\pi}6\) 

(3) \(\frac{5\pi}{12},\frac{7\pi}{12}\) 

(4) \(\frac{7\pi}{12},\frac{11\pi}{12}\)

Answer 1

Correct option is (4) \(\frac{7\pi}{12},\frac{11\pi}{12}\) 

 \(\begin{vmatrix}1+sin^2x&sin^2x&sin^2x\\cos^2x&1+cos^2x&cos^2x\\4sin2x&4sin2x&1+4sin2x\end{vmatrix}\) = 0

use R₁ → R₁ → R₂ →R₃