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Byju's Answer
Standard XII
Mathematics
Trigonometric Ratios of Multiples of an Angle
Prove that ...
Question
Prove that
tan
α
=
sin
2
α
1
+
cos
2
α
and hece deduce the values of
tan
15
o
and
tan
22
1
2
o
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Solution
s
i
n
2
α
1
+
c
o
s
2
α
=
s
i
n
2
α
s
i
n
2
α
+
c
o
s
2
α
+
c
o
s
2
α
−
s
i
n
2
α
=
2
s
i
n
α
c
o
s
α
2
c
o
s
2
α
=
t
a
n
α
t
a
n
15
=
s
i
n
2
(
15
)
1
+
c
o
s
2
(
15
)
=
s
i
n
30
1
+
c
o
s
30
=
1
2
+
√
3
t
a
n
22
1
2
=
s
i
n
45
1
+
c
o
s
45
=
1
1
+
√
2
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Similar questions
Q.
Prove that:
tan
(
α
+
β
)
+
tan
(
α
−
β
)
=
sin
2
α
1
−
sin
2
α
−
sin
2
β
Q.
If
cos
α
+
cos
β
+
cos
α
=
0
=
sin
α
+
sin
β
+
sin
α
prove that
cos
2
α
+
cos
2
β
+
cos
2
α
=
3
α
=
sin
2
α
+
sin
2
β
+
sin
2
α
Q.
If
A
+
B
=
45
∘
, prove that
(
1
+
tan
A
)
(
1
+
tan
B
)
=
2
and hence deduce that
tan
22
1
2
∘
=
√
2
−
1
Q.
If tan
β
=
tan
α
+
tan
γ
1
+
tan
α
tan
γ
,
Prove that:
sin
2
β
=
sin
2
α
+
sin
2
γ
1
+
sin
2
α
sin
2
γ
Q.
Prove that
cos
2
α
cos
2
β
+
sin
2
(
α
−
β
)
−
sin
2
(
α
+
β
)
=
cos
2
(
α
+
β
)
.
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Standard XII Mathematics
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