Question

If $sin 2 A=\frac{1}{2}$ and $sin 2 B=-\frac{1}{2},$ then which of the following is false?

• A. $sin \left(A + B\right)$ may be $0$
• B. $cos \left(A - B\right)$ may be $0$
• C. $sin \left(A + B\right)$ or $cos \left(A - B\right)$ is zero
• D. $sin \left(A + B\right)=0$

Answer 1

Answer: (D)

$sin 2 A=\frac{1}{2},sin ⁡ 2 B=-\frac{1}{2}$
$\Rightarrow sin 2 A+sin ⁡ 2 B=0$
$\Rightarrow 2sin \left(A + B\right)cos ⁡ \left(A - B\right)=0$
$\Rightarrow sin \left(A + B\right)=0$ or $cos \left(A - B\right)=0$
Hence, $4^{th}$ option is false.