Question

If $A$ and $B$ are acute positive angles satisfying the equations $3{\sin }^{2}A+{\cos }^{2}B=1$ and $\sin 3B=0$, then $A+B=$

• A. $\frac{2\pi }{3}$
• B. $\frac{\pi }{2}$
• C. $\frac{\pi }{4}$
• D. $\frac{\pi }{3}$

Answer 1

The correct option is B $\frac{\pi }{2}$

$3{\sin }^{2}A+{\cos }^{2}B=1$ --------(1)
$\sin 3B=0$
Since $B$ is an acute angle.
$\therefore 3B=\pi \Rightarrow B=\frac{\pi }{3}$
Substitute $B=\frac{\pi }{3}$ in equation (1)
$3{\sin }^{2}A+\frac{1}{4}=1\Rightarrow \sin A=\frac{1}{2}$
Since A is an acute angle.
$\therefore A=\frac{\pi }{6}$
$\therefore A+B=\frac{\pi }{2}$
Ans: B