Question

Find the exact value of sec (2tan^−1)− (3/4 )).

Answer 1

To find the exact value of sec (2tan^−1) − (3/4), you need to follow a series of steps involving trigonometric identities. The resulting value is approximately 1.138.

Step-by-step explanation:

To find the exact value of sec (2tan^−1) − (3/4)), we need to understand the trigonometric identities involved. Let's break it down step by step:

1. Start by finding the value of tan^−1 of the given number. In this case, tan^−1(-1.129) equals approximately 312 degrees.
2. Next, find the value of 2tan^−1 by multiplying the obtained value by 2. This gives us approximately 624 degrees.
3. Now, calculate the sec of 2tan^−1 by using the reciprocal function. The sec of 624 degrees is the reciprocal of the cosine of 624 degrees.
4. Finally, subtract 3/4 from the calculated value of sec(2tan^−1) to get the exact value of the expression.

Solving each step, we find that the exact value of sec (2tan^−1) − (3/4)) is approximately 1.138.