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Byju's Answer
Standard XII
Mathematics
Sum of Trigonometric Ratios in Terms of Their Product
Prove x 2x-...
Question
Prove
cot
x
cot
2
x
−
cot
2
x
cot
3
x
−
cot
3
x
cot
x
=
1
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Solution
LHS
c
o
t
x
cot
2
x
−
cot
2
x
cot
3
x
−
cot
3
x
c
o
t
x
⇒
1
t
a
n
x
tan
2
x
−
1
tan
2
x
tan
3
x
−
1
tan
3
x
t
a
n
x
⇒
tan
3
x
−
t
a
n
x
−
tan
2
x
t
a
n
x
tan
2
x
tan
3
x
⇒
tan
3
x
−
(
t
a
n
x
+
tan
2
x
)
t
a
n
x
tan
2
x
tan
3
x
∵
tan
(
A
+
B
)
=
t
a
n
A
+
t
a
n
B
1
−
t
a
n
A
t
a
n
B
⇒
tan
3
x
−
tan
(
3
x
)
(
1
−
t
a
n
x
tan
2
x
)
t
a
n
x
tan
2
x
tan
3
x
⇒
tan
3
x
−
tan
3
x
+
t
a
n
x
tan
2
x
tan
3
x
t
a
n
x
tan
2
x
tan
3
x
=
1
=
RHS Hence proved.
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12
Similar questions
Q.
Prove that cot
x
cot 2
x
– cot 2
x
cot 3
x
– cot 3
x
cot
x
= 1