solve 2cosx+2sinx=√6
Answers
Factor out a 2:
2
(
cos
x
+
sin
x
)
=
√
6
cos
x
+
sin
x
=
√
6
2
Square both sides:
(
cos
x
+
sin
x
)
2
=
(
√
6
2
)
2
cos
2
x
+
2
sin
x
cos
x
+
sin
2
x
=
6
4
Apply the identity
sin
2
x
+
cos
2
x
=
1
:
1
+
2
sin
x
cos
x
=
6
4
Apply the identity
2
sin
x
cos
x
=
sin
2
x
:
sin
2
x
=
1
2
2
x
=
30
˚
and
2
x
=
150
˚
x
=
15
˚
and
75
˚
Check both solutions in the original equation. Both work. Hence, our solution set is
{
15
˚
,
75
˚
}
.
Answer:
The solutions in the given interval are x = 15 and x =75˚.
Step-by-step explanation:
Explanation:
Factor out a 2:
2(cosx+sinx) =√6
cosx+sinx =√6/2
Square both sides:
(cosx+sinx)² =(√6/2)²
cos²x+2sinx cosx + sin²x= 6/4
Apply the identity sin²x +cos²x=1 :
1+2sinx cosx =6/4
Apply the identity
2sinx cosx = sin2x :
sin2x = 1/2
2x = 30˚and 2x =150˚
x=15˚and75˚
Check both solutions in the original equation. Both work. Hence, our solution set is {15˚,75˚} .
Hopefully this helps!