Angle Sum Property Of A Triangle

We are given a triangle where the angles , , and are in A.P. This implies:
Therefore, Next, we need to find the expression for , where , , and are the sides opposite to angles , , and , respectively.
Step 1: Use the Law of Sines.
By the Law of Sines, we know: From this, we can express the sides in terms of the sine of the angles: where is the common constant, .
Step 2: Expression for .
We need to find: Simplifying: Using the sum of sines identity: Therefore, the expression becomes: Since , we have: Thus, the correct answer is .