Question

The equation ${\sin }^{2}x=\frac{a^2+b^2}{2ab}$ is possible if

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

Answer 1

The correct option is A $a=b$

${\sin }^{2}x=\frac{a^2+b^2}{2ab}$

Now, $\sin x\le 1$

${\sin }^{2}x\le 1$

$\frac{a^2+b^2}{2ab}\le 1$

$a^2+b^2\le 2ab$

Or $a^2+b^2-2ab\le 2ab-2ab$ $\Rightarrow {(a-b)}^2\le 0$

Hence, the answer is $a=b.$