Question: If 4 tanB = 3, then find the value of the following expression?

To find the value of the expression, we need to use the given information that 4 tanB = 3. Let's break down the problem into steps to determine the value of the expression.

Step 1: Understand the given information
The given information states that 4 tanB = 3. This equation relates the tangent of angle B to a numerical value of 3/4.

Step 2: Recall the definition of tangent
The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side in a right triangle.

Step 3: Set up a right triangle
Since the tangent is defined in terms of a right triangle, we can create a right triangle with angle B and label the sides accordingly. Let's assume that the side opposite angle B is represented by 'y' and the adjacent side is represented by 'x'.

Step 4: Apply the given information to the right triangle
Based on the given information, we know that 4 tanB = 3. Since the tangent is the ratio of the side opposite to the side adjacent, we can write this as y/x = 3/4.

Step 5: Solve for the unknown sides
To find the value of the expression, we need to determine the values of 'x' and 'y' in the right triangle. We can rearrange the equation from step 4 to solve for 'y' in terms of 'x': y = (3/4)x.

Step 6: Substitute the values into the expression
Now that we have the relationship between 'y' and 'x', we can substitute this into the expression to find its value. The expression is not provided in the question, so we cannot provide the specific value. However, you can substitute the appropriate values of 'x' and 'y' into the expression to calculate its value.

Overall, the value of the given expression can be found by setting up a right triangle, applying the given information, solving for the unknown sides, and substituting those values into the expression.