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Byju's Answer
Standard XII
Mathematics
Composite Function
Prove that si...
Question
Prove that sin2x+ sin2(x+π/3)+sin2(x-π/3)=3/2
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Solution
sin^2x + (sinx cospi/3 + cosx sinpi/3)^2 + (sinx cos pi/3 - cosx sinpi/3)^2
sin^2 x + (2sin^2x cos^2 pi/x) + (2cos^x sin^ pi/3)
sin^2 x + 1/2 sin^x + 3/2(1-sin^2 x)
3/2 sin^2 x + 3/2 - 3/2 sin^ x
3/2 = Answer
hence proved
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24
Similar questions
Q.
Evaluate:
sin
2
x
+
sin
2
(
x
+
π
3
)
+
cos
(
x
+
π
2
)
cos
x
Q.
If
f
(
x
)
=
s
i
n
2
x
+
s
i
n
2
(
x
+
π
3
)
+
c
o
s
x
c
o
s
(
x
+
π
3
)
a
n
d
g
(
5
4
)
=
1
, then (gof)(x)=
Q.
f
(
x
)
=
s
i
n
2
x
+
s
i
n
2
(
x
+
π
3
)
+
c
o
s
(
x
+
π
3
)
c
o
s
x
and
g
(
5
4
)
=
1
then
g
(
f
(
x
)
)
is
Q.
The period of the function
f
(
x
)
=
c
⎡
⎢
⎣
sin
2
x
+
sin
2
(
x
+
π
3
)
+
cos
x
cos
(
x
+
π
3
)
⎤
⎥
⎦
is (where
c
is constant)
Q.
Assertion :
f
(
x
)
=
sin
2
x
+
sin
2
(
x
+
π
3
)
+
cos
x
cos
(
x
+
π
3
)
then
f
′
(
x
)
=
0
Reason: Derivative of a constant function is always zero
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