Question

In an isosceles right angled triangle, a straight line drawn from the min-point of one of equal sides to the opposite angle. It divides the angle into two parts, $\theta$ and $(\frac{\pi }{4}-\theta )$. Then $\tan \theta$ and $\tan (\frac{\pi }{4}-\theta )$ are equal to :

• A. $\frac{1}{3},\frac{1}{4}$
• B. $\frac{1}{4},\frac{1}{5}$
• C. $\frac{1}{5},\frac{1}{6}$
• D. $\frac{1}{2},\frac{1}{3}$

Answer 1

The correct option is D $\frac{1}{2},\frac{1}{3}$

From the given condition,
$\tan \theta =\frac{\frac{side}{2}}{side}$ ... since it is an isosceles right angled triangle. Hence both sides will be equal.
Therefore
$\tan \theta =\frac{1}{2}$
Now
$\tan (\frac{\pi }{4}-\theta )$
$=\frac{1-\tan \theta }{1+\tan \theta }$
$=\frac{1-\frac{1}{2}}{1+\frac{1}{2}}$
$=\frac{1}{3}$