tan^-1 1/2 +tan^-1 3/2
You asked:
Evaluate the expression: \(\frac{\arctan\left( 1 \right)}{2} + \frac{\arctan\left( 3 \right)}{2}\)
MathBot Answer:
\[\frac{\arctan\left( 1 \right)}{2} + \frac{\arctan\left( 3 \right)}{2} = \frac{\pi}{8} + \frac{\arctan{\left(3 \right)}}{2} \approx 1.01722196789785136772278896155048\]
\[\begin{aligned}\frac{\arctan\left( 1 \right)}{2} + \frac{\arctan\left( 3 \right)}{2}& = \arctan{\left(1 \right)} \cdot \frac{1}{2} + \arctan{\left(3 \right)} \cdot \frac{1}{2}\\& = \frac{\pi}{4} \cdot \frac{1}{2} + \arctan{\left(3 \right)} \cdot \frac{1}{2}\\& = \frac{\pi}{8} + \arctan{\left(3 \right)} \cdot \frac{1}{2}\\& = \frac{\pi}{8} + \frac{1}{2} \cdot \arctan{\left(3 \right)}\\& = \frac{1}{2} \cdot \arctan{\left(3 \right)} + \frac{\pi}{8}\end{aligned}\]