Question 541147
{{{sin(theta)= cos(2theta+60)}}}
With the tip, it transforms into
{{{cos(90-theta)=cos(2theta+60)}}}
If two angles are the same, they have the same cosine.
So at least we'll get a solution from {{{90-theta=2theta+60}}}
Adding {{{theta}}} to both sides, we get {{{90=3theta+60}}}
Subtracting 60 from both sides, we get {{{30=3theta}}}
Dividing both sides by 3, we get {{{10=theta}}}
So {{{theta=10degrees}}} is a solution.
Are there others?
Could the cosines be equal, but the angles be different?
In general, that could happen, but since {{{theta}}} is an acute angle
{{{0<theta<90}}} --> {{{90-0>90-theta>90-90}}} --> {{{90>90-theta>0}}}
So 90-{{{theta}}}; is an acute angle too. That means its cosine is a positive number.
{{{0<theta<90}}} --> {{{0<2theta<180}}} ---> {{{60<2theta+60<240}}}
The angle {{{2theta+60}}} seems to have more options, but since its cosine is equal to a positive number, it is more restricted.
The only cosines that area positive for angles between 60° and 240° are those for angles between 60° and 90°. Between 90° and 270° they are negative.