Find all solutions in the interval [0,2π)

Calculus
Tutor: None Selected Time limit: 1 Day

tan(a/2) = sin(a)

Mar 17th, 2015

tan(a/2) = +/-sqrt[(1-cosa)/1+cosa) = sin(a)

Square both sides to get

(1 - cosa)/(1+cosa) = sin^2a    but sin^2a = 1 - cos^2a

So,  (1 - cosa)/(1+cosa) = 1 - cos^2 = (1 + cosa)(1 - cosa)

therefore,

(1+cosa)^2 = 1

1+cosa = 1

cosa = 0

a = pi/2, 3pi/2

Mar 17th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Mar 17th, 2015
...
Mar 17th, 2015
Mar 25th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer