Question

If $x=ta{n}^{-1}\frac{1}{7}$ and $y=ta{n}^{-1}\frac{1}{3}$, then

• A. cos 2x = sin 4y
• B. cos 4y = cos 2x
• C. cos 2y = sin 4x
• D. None of these

Answer 1

The correct option is A cos 2x = sin 4y

$x=ta{n}^{-1}\frac{1}{7}\Rightarrow tanx=\frac{1}{7}$
and
$y=ta{n}^{-1}\frac{1}{3}\Rightarrow tany=\frac{1}{3}$
Now,
$cos2x=\frac{1-ta{n}^{2}x}{1+ta{n}^{2}x}=\frac{24}{25}$
$sin4y=2sin2ycos2y=\frac{2.2tany(1-ta{n}^{2}y)}{(1+ta{n}^{2}y{)}^2}=\frac{24}{25}\therefore cos2x=sin4y$