How do you find the value of tan (A - B) if cos A = 3/5 and sin B = 5/13, and A and B are in Quadrant I?

1 Answer
Nghi N.
May 24, 2016

33/16

Explanation:

First, find tan A and tan B.
cos A = 3/5 --> sin^2 A = 1 - 9/25 = 16/25 --> cos A = +- 4/5
cos A = 4/5 because A is in Quadrant I
tan A = sin A/(cos A) = (4/5)(5/3) = 4/3.

sin B = 5/13 --> cos^2 B = 1 - 25/169 = 144/169 --> sin B = +- 12/13.
sin B = 12/13 because B is in Quadrant I
tan B = sin B/(cos B) = (5/13)(13/12) = 5/12
Apply the trig identity:
tan (A - B) = (tan A - tan B)/(1 - tan A.tan B)
tan A - tan B = 4/3 - 5/12 = 11/12
(1 - tan A.tan B) = 1 - 20/36 = 16/36 = 4/9
tan (A - B) = (11/12)(9/4) = 33/16

Related questions
See all questions in Trigonometric Functions of Any Angle
Impact of this question
77029 views around the world
You can reuse this answer
Creative Commons License