Question

Find the general solution to the following sin(theta)cos2(theta)+sin(theta)=1+cos2(theta)

Answer 1

sinxcos2x + sinx = 1+cos2x
sinx(1+cos2x) = 1+cos2x
sinx(1+cos2x) - (1+cos2x) = 0
(1+cos2x)(sinx-1) = 0
for zeros, take 1+cos2x=0 or sinx-1=0
* 1+cos2x=0
cos2x=-1
cos2x=cos(k*2pi +- pi)
2x=k*2pi +- pi
x = k*pi +- pi/2

** sinx-1=0
sinx = 1
sinx = sin pi/2
sinx =sin(k*2pi + pi/2)
x =k*2pi + pi/2

Answer 2

thank you so much

Answer 3

welcome

Answer 4

i have a question on the first problem why is it a negative instead of a positive if cos(pi)=-1?