The trigonometric equation is .
Pythagorean identity : .
Apply zero product property.
\ or
or
.
Solve .
The general solution of is
, where
is an integer.
The solution is , where
is an integer.
Find the solutions on the interval .
If ,
.
If ,
.
Thus, the solutions of are
and
on the interval
.
Solve .
The general solution of is
, where
is an integer.
The solution is , where
is an integer.
Find the solutions on the interval .
If ,
.
If ,
.
Thus, the solutions of are
and
on the interval
.
\
Therefore, the solutions of are
,
,
and
on the interval
.
Check :
\The equation is .
Substitute in
.
Since the above statement is true, is a solution of
.
\
Substitute in
.
Since the above statement is true, is a solution of
.
\
Substitute in
.
Since the above statement is true, is a solution of
.
\
Substitute in
.
Since the above statement is true, is a solution of
.
The solutions of are
,
,
and
on the interval
.