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Byju's Answer
Standard XII
Physics
Phase and the General Equation
Find the magn...
Question
Find the magnitude of minimum value of
1
+
2
sin
x
+
3
cos
2
x
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Solution
1
+
2
sin
x
+
3
cos
2
x
=
−
3
sin
2
x
+
2
sin
x
+
4
=
−
3
(
sin
2
x
2
sin
x
3
)
+
4
=
−
3
(
sin
x
−
1
3
)
2
+
13
3
Now
0
≤
(
sin
−
1
3
)
2
≤
16
9
⇒
−
16
3
≤
−
3
(
sin
x
−
1
3
)
2
≤
0
Adding
13
3
to the equation,
−
1
≤
−
3
(
sin
x
−
1
3
)
2
+
13
3
≤
13
3
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2
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