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Byju's Answer
Standard XII
Mathematics
Conditional Identities
Prove that ...
Question
Prove that
cot
x
.
cot
2
x
−
cot
2
x
.
cot
3
x
−
cot
x
.
cot
3
x
=
1
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Solution
cot x cot 2x - cot 2x cot 3x - cot 3x cot 4x
= cot x cot 2x - cot 3x (cot 2x+ cot x)
= cot x cot 2x - cot (2x+x)(cot 2x+ cot x)
[ as
c
o
t
(
A
+
B
)
=
c
o
t
A
c
o
t
B
−
1
c
o
t
A
c
o
t
B
]
= cot x cot 2x-
(
c
o
t
2
x
c
o
t
x
−
1
c
o
t
x
+
c
o
t
2
x
)
(cot 2x+ cot x)
= cot x cot 2x- (cot 2x cot x-1)
= cot x cot 2x- cot 2x cot x+1
= 1
Hence, proved
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