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Byju's Answer
Standard XII
Mathematics
General Solution of Trigonometric Equation
Prove that si...
Question
Prove that
s
i
n
4
θ
−
c
o
s
4
θ
=
1
−
2
c
o
s
2
θ
[3 MARKS]
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Solution
Formula: 2 Marks
Application: 1 Mark
Consider
s
i
n
4
θ
−
c
o
s
4
θ
=
(
s
i
n
2
θ
)
2
−
(
c
o
s
2
θ
)
2
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
=
(
s
i
n
2
θ
+
c
o
s
2
θ
)
(
s
i
n
2
θ
−
c
o
s
2
θ
)
=
1
(
s
i
n
2
θ
−
c
o
s
2
θ
)
[
∵
s
i
n
2
θ
+
c
o
s
2
θ
=
1
]
=
s
i
n
2
θ
−
c
o
s
2
θ
=
(
1
−
c
o
s
2
θ
)
−
c
o
s
2
θ
[
s
i
n
2
θ
=
1
−
c
o
s
2
θ
]
=
1
−
2
c
o
s
2
θ
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