If sin 2 A=(1/2) and sin 2 B=-(1/2), then which of the following is false?

Question

If sin 2 A=(1/2) and sin 2 B=-(1/2), then which of the following is false? (A) sin (A + B) may be 0 (B) cos (A - B) may be 0 (C) sin (A + B) or cos (A - B) is zero (D) sin (A + B)=0

Tardigrade Admin · Accepted Answer

sin 2 A=(1/2),sin â¡ 2 B=-(1/2) ⇒ sin 2 A+sin â¡ 2 B=0 ⇒ 2sin (A + B)cos â¡ (A - B)=0 ⇒ sin (A + B)=0 or cos (A - B)=0 Hence, 4th option is false.

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

$s in (A + B)$ may be $0$

$cos (A - B)$ may be $0$

$s in (A + B)$ or $cos (A - B)$ is zero

$s in (A + B) = 0$

$s in 2 A = \frac{1}{2}, s in 2 B = - \frac{1}{2}$
$\Rightarrow s in 2 A + s in 2 B = 0$
$\Rightarrow 2 s in (A + B) cos (A - B) = 0$
$\Rightarrow s in (A + B) = 0$ or $cos (A - B) = 0$
Hence, $4^{t h}$ option is false.

Q. If sin2A=21​ and sin2B=−21​, then which of the following is false?

sin(A+B) may be 0

cos(A−B) may be 0

sin(A+B) or cos(A−B) is zero

sin(A+B)=0