Inverse Trigonometric Functions

Step 1: Evaluate .
The value of is the angle whose tangent is . We know that: So,

Step 2: Evaluate .
The value of is the angle whose secant is . The secant function is the reciprocal of the cosine function, so we are looking for the angle whose cosine is . This corresponds to the angle:

Step 3: Subtract the two values.
Now, we subtract the two values we calculated:

Step 4: Conclusion.
The correct answer is (D) .

Step 1: Simplify the inverse sine.
So,

Step 2: Apply tangent function.
Taking tangent on both sides:

Final Answer:

Step 1: Recall the identity for inverse trigonometric functions.
We know that: However, for negative values of , the identity adjusts based on the quadrant.

Step 2: Simplify the expression.
Given expression is: First, use the identity for inverse tangent and cotangent:

Step 3: Conclusion.
Thus, the value is: So, the correct answer is (C) .

Step 1: Let

Step 2: Use reciprocal identity.

Final Answer: