Question

Given: sin(A) = 5/13, pi/2 < A < pi and tan (B) = - sqrt 13, pi/2 < B < pi

What is tan(A - B)?

A. (5 + 12sqrt13)/(12 - 5sqrt13)
B. (12 - 5sqrt13)/(5 + 12sqrt13)
C. (12 + 5sqrt13)/(-5 + 12sqrt13)
D. (-5 + 12sqrt13)/(12 + 5sqrt13)

Answer 1

Answer:

The answer is D

Step-by-step explanation:

I got it right on edge 2021

Answer 2

Using the trigonometric Identities, tan(A - B) = $\frac{-5+12\sqrt{13} }{12+5\sqrt{13} }$

What are trigonometric identities?

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

Given

sin(A) = $\frac{5}{13}$

$\frac{\pi }{2} < A < \pi$

Using the trigonometric identity

$sin^{2}A +cos^{2}A=1$

cosA = $\sqrt{1-sin^{2}A }$

cosA = $\sqrt{1-(\frac{5}{13} )^{2} }$

cosA = $-\frac{12}{13}$

tan A = $\frac{sinA}{cosA}$

tanA = $\frac{\frac{5}{13} }{\frac{-12}{13} }$

tanA = $-\frac{5}{12}$

tan(A-B) = $\frac{tanA-tanB}{1+tanAtanB}$

= $\frac{-\frac{5}{12} -(-\sqrt{13}) }{1+(-\frac{5}{12})(-\sqrt{3}) }$

= $\frac{5-12\sqrt{13} }{-12-5\sqrt{3} }$

= $\frac{-5+12\sqrt{13} }{12+5\sqrt{13} }$

Option D is correct.

Hence, tan(A - B) = $\frac{-5+12\sqrt{13} }{12+5\sqrt{13} }$

Find out more information about trigonometric Identities here

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