Can you solve (sintheta) (cottheta) - cos^2theta = 0 ?

1 Answer
Mar 31, 2018

#theta=pi/2+npi, theta=2npi# where #n# is any integer.

Explanation:

It is best to convert this equation to one trigonometric function.

Recall that #cottheta=costheta/sintheta#

We then have

#cancelsintheta(costheta/cancelsintheta)-cos^2theta=0#

#costheta-cos^2theta=0#

Factor out a cosine:

#costheta(1-costheta)=0#

We now must solve #costheta=0, 1-costheta=0#

For #costheta=0, theta=pi/2+npi#, as cosine is equal to zero for #pi/2, 3pi/2, (5pi)/2, (7pi)/2,..,(pi)/2+npi#.

For #1-costheta=0:#

#-costheta=-1#

#costheta=1#

#theta=2npi# as #costheta=1# for #theta=0, 2pi, 4pi, 6pi,...,2npi#