Question

Given: Sine (A) = StartFraction 5 Over 13 EndFraction, StartFraction pi Over 2 EndFraction < A < Pi and Tangent (B) = negative StartRoot 13 EndRoot, StartFraction pi over 2 EndFraction < B < Pi What is tan(A – B)?.

Answer 1

The value of Tan(A - B) is -0.1295.

Trigonometry

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

Right angle triangle

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

Given

Sin A = 5 ÷ 13 and Tan B = -√3.

To find

The value of tan(A - B).

How to find the value of tan(A - B)?

The angle A will be,

$\begin{aligned} \rm sin A &= \dfrac{5}{13}\\\\\rm A &= \rm sin^{-1} \dfrac{5}{13}\\\\\rm A &= 22.62^o\\\\\end{aligned}\\But\ for\ the\ \dfrac{\pi}{2} < A < \pi\\\\A = 22.62^o + 90^o\\\\A = 112.62^o$

Similarly for angle B,

$\begin{aligned} \rm tan B &= -\sqrt{3} \\\\\rm B &= \rm tan^{-1} -\sqrt{3} \\\\\rm B &= -60^o\\\\\end{aligned}\\\rm But\ for\ the\ \dfrac{\pi}{2} < B < \pi\\\\B = -60^o + 180^o\\\\B = 120^o$

Then tan (A - B) will be

Tan(A - B) = tan(112.62 - 120)

Tan(A - B) = tan(-7.38)

Tan(A - B) = -0.1295

Thus, the value of Tan(A - B) is -0.1295.

More about the trigonometry link is given below.

brainly.com/question/13710437