How do I find all the solutions for cos(x)tan(x)=tan(x) on one interval rotation of the unit circle?

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Answer 1 · 2017-10-19T01:30:17

In #[0, 2pi)#, we have #x in 0 and pi#

We can immediately rewrite as

#0 = tanx - cosxtanx#

#0 = tanx(1 - cosx)#

So we now have two equations.

#tanx = 0#

#x = 0 or pi#

AND

#1 - cosx= 0#

#x = 0#

So in the interval #[0, 2pi)#, the solutions will be #x in 0 uu pi#

Hopefully this helps!