find all solutions on the interval (0,2p) by first multiplying to rid the denominator, and then squaring both sides. (sinx)/(1+cosx) =1

Question

find all solutions on the interval (0,2π) by first multiplying to rid the denominator, and then squaring both sides.

Answer 1

sinx/(1+cosx)=1

 

(sinx/(cosx+1))-1=0

 

(sinx-1-cosx)/(1+cosx)=0

 

Set the denominator to zero.

 

1+cosx=0

cosx=-1

 

x = pi .  This value will make the function undefined.

 

Solution = (0,pi/2]