Use an addition or subtraction formula to write the expression as a trigonometric function of one number:
tan75degrees-tan15degrees/1+tan75tan15=tanAdegrees =square root B
Its asking for the value of A and B. I know A =60 degrees, what I can't figure out is B, I don't understand what its asking for
draw a right triangle, 2,1, sqrt3
What is the tan of 60 deg?
To find the value of B, we need to simplify the expression and rewrite it in terms of trigonometric functions of a single angle. Let's break it down step by step:
1. Start with the given expression:
tan(75°) - tan(15°) / (1 + tan(75°)tan(15°)) = tan(A°) = √B
2. We can rewrite the tangent of the difference of two angles using the subtraction formula:
tan(A - B) = (tanA - tanB) / (1 + tanA*tanB)
Using this formula, we can rewrite the given expression as:
tan(75° - 15°) / (1 + tan(75°)tan(15°)) = tan(A°) = √B
3. Simplify the expression:
tan(60°) / (1 + tan(75°)tan(15°)) = tan(A°) = √B
Since we know that A = 60°, we have:
tan(60°) = √B
Now, we need to solve for B.
4. Evaluate the tangent of 60°:
tan(60°) = √3
So, we can substitute √3 for tan(60°):
√3 = √B
To get B, we square both sides of the equation:
3 = B
Therefore, the value of A is 60° and the value of B is 3.