SOLUTION: How to do it: If theta and beta belong to Q1, and cot theta = 12/13, sin beta = √ 2/2, tan (theta + beta) is equal to: a) - 20 b) 20 c) 25 d) - 25

Algebra ->  Trigonometry-basics -> SOLUTION: How to do it: If theta and beta belong to Q1, and cot theta = 12/13, sin beta = √ 2/2, tan (theta + beta) is equal to: a) - 20 b) 20 c) 25 d) - 25      Log On


   



Question 825051: How to do it: If theta and beta belong to Q1, and cot theta = 12/13,
sin beta = √ 2/2, tan (theta + beta) is equal to:
a) - 20
b) 20
c) 25
d) - 25

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
How to do it: If theta and beta belong to Q1, and cot theta = 12/13,
sin beta = √ 2/2, tan (theta + beta) is equal to:
***
letx=theta
lety=beta
Identity: tan(x+y)=%28tan%28x%29%2Btan%28y%29%29%2F%281-tan%28x%29tan%28y%29%29
..
cotx=12/13 (given)
tanx=13/12
..
siny=√2/2 (working with a 45˚ right triangle)
tany=1
..
tan(x+y)=%2813%2F12%2B1%29%2F%281-13%2F12%2A1%29=%2825%2F12%29%2F%281%2F12%29=25
ans: c)25