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

Did you know? You can earn $20 for every friend you invite to Studypool!
Click here to
Refer a Friend
...
Mar 17th, 2015
...
Mar 17th, 2015
Dec 11th, 2016
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