Question

When simplified, tan(40°)-tan(10°)/1+(tan(40°))tan(10°)) is equivalent to which expression?

a. tan(-50°)
b. tan(-30°)
c. tan (30°)
d. tan(50°)

Answer 1

When simplified, the expression is equivalent to approx. 0.5778, which is closest to the tangent of 30°.

Step-by-step explanation:

First, we will simplify the expression by substituting the given values of the angles:

tan(40°) - tan(10°) / (1 + tan(40°)tan(10°))

Next, we will calculate the values of the tangents:

tan(40°) = 0.8391
tan(10°) = 0.1763

Now, substitute the calculated values into the expression:

0.8391 - 0.1763 / (1 + 0.8391 * 0.1763)

Simplifying further:

0.8391 - 0.1763 / (1 + 0.1478)

Calculating the numerator:

0.6628 / 1.1478

Dividing, we get:

0.5778

Therefore, the expression is equivalent to approx. 0.5778, which is closest to the tangent of 30°, so the answer is c. tan(30°).