Trigonometric Identities

We are given the equation: Using the following trigonometric identities: Substituting these into the equation: Simplifying: Now, , so the equation becomes: Rearranging the terms: Simplifying further, we find that the value of is . Hence, the correct value is . Thus, the answer is .

We are given the expression , which is a difference of cubes. We can factor it using the identity: Thus, we can factor as: We know that , so the expression becomes: Now, we simplify the second factor. Using the identity , we rewrite as: Thus, the second factor becomes: Finally, we recognize that , so the expression simplifies to: Thus, the correct answer is .

We are given that , and we are asked to find an expression for . Step 1: Use sum and difference trigonometric identities First, recall the trigonometric identity for the cotangent of a sum: We can relate this to the given equation using angle sum identities. Step 2: Manipulate the equation and simplify Using the relationship between and , and simplifying using the angle sum identities, we find that: Thus, the correct answer is .