Question

The equation $(a + b)^{2} = 4ab\sin^{2}\theta$is possible only when.

• A. $2a = b$
• B. $a = b$
• C. $a = 2b$
• D. None of these

Answer 1

Answer: (B)

$a = b$

Answer 2

We have $(a + b)^{2} = 4ab\sin^{2}\theta$

$\Rightarrow \sin^{2}\theta = \frac{(a + b)^{2}}{4ab} \leq 1 \Rightarrow (a + b)^{2} - 4ab \leq 0$

$\Rightarrow (a - b)^{2} \leq 0 \Rightarrow a = b.$