Questions: Question number 20. If possible, evaluate: 6 arcsin (1)+8 arctan (1) 0 5 π 2 π Undefined π 5 π/2 None of these

Transcript text: Question number 20. If possible, evaluate: $6 \arcsin (1)+8 \arctan (1)$ 0 $5 \pi$ $2 \pi$ Undefined $\pi$ $\frac{5 \pi}{2}$ None of these

Solution

Solution Steps

To evaluate the expression $6 \arcsin (1) + 8 \arctan (1)$, we need to understand the values of $\arcsin(1)$ and $\arctan(1)$.

$\arcsin(1)$ is the angle whose sine is 1. This angle is $\frac{\pi}{2}$.
$\arctan(1)$ is the angle whose tangent is 1. This angle is $\frac{\pi}{4}$.

We then substitute these values into the expression and simplify.

Step 1: Evaluate $\arcsin(1)$

The value of $\arcsin(1)$ is the angle whose sine is 1. This angle is: \[ \arcsin(1) = \frac{\pi}{2} \]

Step 2: Evaluate $\arctan(1)$

The value of $\arctan(1)$ is the angle whose tangent is 1. This angle is: \[ \arctan(1) = \frac{\pi}{4} \]

Step 3: Substitute and Simplify

Substitute the values of $\arcsin(1)$ and $\arctan(1)$ into the expression $6 \arcsin(1) + 8 \arctan(1)$: \[ 6 \arcsin(1) + 8 \arctan(1) = 6 \left(\frac{\pi}{2}\right) + 8 \left(\frac{\pi}{4}\right) \]

Simplify the expression: \[ 6 \left(\frac{\pi}{2}\right) + 8 \left(\frac{\pi}{4}\right) = 3\pi + 2\pi = 5\pi \]