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Byju's Answer
Standard XII
Mathematics
General Solution of Trigonometric Equation
Prove the fol...
Question
Prove the following Identities
tan
α
+
tan
β
cot
α
+
cot
β
=
tan
α
tan
β
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Solution
Taking L.H.S
t
a
n
α
+
t
a
n
β
c
o
t
α
+
c
o
t
β
=
t
a
n
α
+
t
a
n
β
1
t
a
n
α
+
1
t
a
n
β
=
t
a
n
α
t
a
n
β
(
t
a
n
α
+
t
a
n
β
)
t
a
n
β
+
t
a
n
α
=
(
t
a
n
α
)
(
t
a
n
β
)
=
R
.
H
.
S
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Similar questions
Q.
If
a
cos
2
θ
+
b
sin
2
θ
=
c
has α and β as its roots, then prove that
(i)
tan
α
+
tan
β
=
2
b
a
+
c
[NCERT EXEMPLAR]
(ii)
tan
α
tan
β
=
c
-
a
c
+
a
(iii)
tan
α
+
β
=
b
a
[NCERT EXEMPLAR]
Q.
If
a
cos
2
x
+
b
sin
2
x
=
c
has α and β as its roots, then prove that
(i)
tan
α
+
tan
β
=
2
b
a
+
c
[NCERT EXEMPLAR]
(ii)
tan
α
tan
β
=
c
-
a
c
+
a
(iii)
tan
α
+
β
=
b
a
[NCERT EXEMPLAR]
Q.
If
tan
α
−
tan
β
=
m
and
cot
α
−
cot
β
=
n
, then prove that
cot
(
α
−
β
)
=
1
m
−
1
n
Q.
If
a
cos
2
θ
+
b
sin
2
θ
=
c
has
α
and
β
as its solutions ,then show that
tan
α
+
tan
β
=
2
b
c
+
a
,
tan
α
tan
β
=
c
−
a
c
+
a
.
Q.
If
α
+
β
=
γ
and
t
a
n
α
t
a
n
β
=
x
y
,
the prove that sin
(
α
−
β
)
=
x
−
y
x
+
y
s
i
n
γ
.
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