Question

If $\sin 2A = 2\sin A$ is true then $A = $____
${\text{A}}{\text{.}}$ 0
${\text{B}}{\text{.}}$ 30
${\text{C}}{\text{.}}$ 45
${\text{D}}{\text{.}}$ 60

Answer 1

Hint: Question is based on trigonometric double angle formula for $\sin 2A = 2\sin A\cos A$.

Complete step-by-step answer:

Given equation is:

$\sin 2A = 2\sin A$

As a first step bring all terms to LHS.

$\sin 2A - 2\sin A = 0$

As we know that $\sin 2A = 2\sin A\cos A$, putting the formula in above equation we get:
$
  2\sin A\cos A - 2\sin A = 0 \\
  2\sin A\left( {\cos A - 1} \right) = 0 \\
  2\sin A = 0 \\
$
or $\cos A - 1 = 0$

$\sin A = 0$ or $\cos A = 1$

$\sin A = \sin 0$ or $\cos A = \cos 0$

$A = 0$ or $A = 0$

Therefore, the value of $A = 0$.

Note: Whenever this type of problem appears first try to resolve the equation using trigonometric identity, after this we form an equation taking $2\sin A$ as common and after that solve the equation and find the value of $A$. Remember the basic trigonometry identities.