90.1k views
3 votes
Given costheta • csctheta - 2costheta = 0, solve for theta (May be multiple answers)

User Nyteshade
by
8.1k points

1 Answer

0 votes

Factor out
\cos\theta:


\cos\theta\csc\theta-2\cos\theta=\cos\theta(\csc\theta-2)=\cos\theta\left(\frac1{\sin\theta}-2\right)=0

Then either


\cos\theta=0\implies\theta=\frac\pi2+n\pi

or


\frac1{\sin\theta}-2=0\implies\sin\theta=\frac12\implies\theta=\frac\pi6+2n\pi\text{ or }\theta=\frac{5\pi}6+2n\pi

where
n is any integer.

User Ahkam
by
8.9k points

Related questions

asked Jan 15, 2020 41.0k views
Murat asked Jan 15, 2020
by Murat
8.3k points
1 answer
2 votes
41.0k views
asked Aug 19, 2019 228k views
Mike Karp asked Aug 19, 2019
by Mike Karp
7.9k points
1 answer
5 votes
228k views