Question

The number of solutions of the equation $si{n}^{4}x+co{s}^{4}x+3si{n}^{2}xco{s}^{2}x=0$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $0$

${\sin }^{4}x+{\cos }^{4}x+3{\sin }^{2}x{\cos }^{2}x=0\Rightarrow {({\sin }^{2}x+{\cos }^{2}x)}^2-2{\sin }^{2}x{\cos }^{2}x+3{\sin }^{2}x{\cos }^{2}x=0\Rightarrow {\sin }^{2}x{\cos }^{2}x=-1[\because si{n}^{2}x+co{s}^{2}x=1]$]

Since the square of any number is non-negative, so the Left Hand Side is always positive.

However, the Right Hand Side given here is negative.

Thus as the $LHS\ne RHS$, there is no solution for the given equation.

Thus the number of solutions for the above equation is $0$.