SOLUTION: tan x + cot x = 25/12 , find sin x + cos x

Algebra ->  Trigonometry-basics -> SOLUTION: tan x + cot x = 25/12 , find sin x + cos x      Log On


   

Question 804658: tan x + cot x = 25/12 , find sin x + cos x
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
tan x + cot x = 25/12 , find sin x + cos x
***
tan%28x%29%2Bcot%28x%29=25%2F12
tan%28x%29%2B%281%2Ftan%28x%29%29=25%2F12
%28tan%5E2%28x%29%2B1%29%2Ftan%28x%29=25%2F12
%2812tan%5E2%28x%29%2B12%29=25tan%28x%29
12tan%5E2%28x%29-25tan%28x%29%2B12=0
(4tan(x)-3)(3tan(x)-4)
..
tan(x)=3/4
working with (3-4-5) right triangle
sin(x)=3/5
cos(x)=4/5
sin(x)+cos(x)=3/5+4/5=7/5
or
tan(x)=4/3
working with (3-4-5) right triangle
sin(x)=4/5
cos(x)=3/5
sin(x)+cos(x)=4/5+3/5=7/5