Inverse Trigonometric Functions

To solve the given problem, we need to evaluate both sides of the equation and find the value of .

We begin by evaluating the left-hand side of the equation :

1. represents the angle whose secant is . Let this angle be , then:
2. We know that: , hence
3. Then, use the identity for tangent:
4. Thus,

Next, evaluate the right-hand side of the equation :

1. represents the angle whose cosine is . Let this angle be , then:
2. We use the identity for sine:
3. Plug into the identity:
4. Thus,

Now, set the two expressions equal:

2. Square both sides to eliminate the square root:
3. Add 1 to both sides:
4. Solve for :

Hence, the value of is , which matches with the provided correct option.