The Trigonometric equation is .
Substitute the double angle formula
\ \
\ \
\ \
Since .
\ \
\ \
Apply zero rule property. \ \
and
\ \
First part .
The general solution of is
, where
is any integer. \ \
For ,
For ,
.
For ,
.
Therefore, the solutions in the interval are
.
Second part
Apply zero rule property. \ \
\ and
and
The general solution of is
, where
is any integer.
solution is
Substitute in
, hence
Substitute in
, hence
Substitute in
, hence
\ \
hence,
Therefore, the solutions in the interval are
.
Consider .
The solution set is .
Therefore, the solution is
\ and
For complete solution we need to combine above two solutions
\Combine solutions is
Arrange in ascending order
\The solution set for is
.