1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Cos(A+B)Cos(A-B)
Prove that ...
Question
Prove that
tan
α
+
tan
β
+
tan
γ
−
tan
α
tan
β
tan
γ
=
sin
(
α
+
β
+
γ
)
cos
α
cos
β
cos
γ
Open in App
Solution
sin
(
α
+
β
+
γ
)
=
sin
(
α
+
β
)
cos
γ
+
cos
(
α
+
β
)
sin
γ
=
sin
α
cos
β
cos
γ
+
cos
α
sin
β
cos
γ
+
cos
α
cos
β
sin
γ
−
sin
α
sin
β
sin
γ
Now divide each term by
cos
α
cos
β
cos
γ
Then Lhs=
tan
α
+
tan
β
+
tan
γ
−
tan
α
tan
β
tan
γ
LHS=RHS
Hence proved.
Suggest Corrections
0
Similar questions
Q.
If
tan
β
=
2
sin
α
sin
γ
sin
(
α
+
γ
)
, show that
tan
α
,
t
a
n
β
,
t
a
n
γ
are in
H
.
P
.
Q.
If
tan
β
=
2
sin
α
sin
γ
sin
(
α
+
γ
)
show that
tan
α
,
tan
β
,
tan
γ
are in H.P. where
α
≠
0
a
n
d
γ
≠
0
a
n
d
β
≠
π
2
Q.
If
t
a
n
(
α
+
β
−
γ
)
t
a
n
(
α
−
β
+
γ
)
=
t
a
n
γ
t
a
n
β
, then either
s
i
n
(
β
−
γ
)
=
0
or
s
i
n
2
α
+
s
i
n
2
β
+
s
i
n
2
γ
=
0
Q.
If
tan
β
=
2
sin
α
sin
γ
sin
(
α
+
γ
)
, then
tan
α
,
tan
β
,
tan
γ
are in which series where
α
≠
0
a
n
d
γ
≠
0
a
n
d
β
≠
π
2
Q.
If
tan
α
=
1
√
x
(
x
2
+
x
+
1
)
,
tan
β
=
√
x
√
x
2
+
x
+
1
and
tan
γ
=
√
x
−
3
+
x
−
2
+
x
−
1
, then prove that
α
+
β
=
γ
.
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Transformations
MATHEMATICS
Watch in App
Explore more
Cos(A+B)Cos(A-B)
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app