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Byju's Answer
Standard XII
Mathematics
General Solution of Trigonometric Equation
i Show that ...
Question
(i) Show that
t
a
n
9
o
−
t
a
n
27
o
−
t
a
n
63
o
+
t
a
n
81
o
=
4
(ii) Show that
c
o
s
42
o
+
c
o
s
78
o
+
c
o
s
162
o
=
0
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Solution
(i) We know that
t
a
n
θ
=
c
o
t
(
90
−
θ
)
=>
t
a
n
81
=
c
o
t
9
and
t
a
n
63
=
c
o
t
27
We need to simplify
t
a
n
9
+
c
o
t
9
−
t
a
n
27
−
c
o
t
27
=>
s
i
n
9
c
o
s
9
+
c
o
s
9
s
i
n
9
−
s
i
n
27
c
o
s
27
−
c
o
s
27
s
i
n
27
=>
1
s
i
n
9.
c
o
s
9
−
1
s
i
n
27.
c
o
s
27
=>
2
2
s
i
n
9.
c
o
s
9
−
2
2
s
i
n
27.
c
o
s
27
=>
2
s
i
n
18
−
2
s
i
n
54
Putting values of
s
i
n
18
=
√
5
−
1
4
,
s
i
n
54
=
√
5
+
1
4
and simplying, we get the expression equal to 4.
(ii)
c
o
s
42
+
c
o
s
78
+
c
o
s
162
=>
c
o
s
(
60
−
18
)
+
c
o
s
(
60
+
18
)
+
c
o
s
162
=>
2
c
o
s
60.
c
o
s
18
+
c
o
s
(
180
−
18
)
=>
2
1
2
c
o
s
18
−
c
o
s
18
=>
0
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0
Similar questions
Q.
Without using tables, show that
tan
9
o
−
tan
27
o
−
tan
63
o
+
tan
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o
=
4
Q.
tan
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Q.
tan
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o
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Q.
Find the value of
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+
tan
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o
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Q.
Show that (i) (ii)
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