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Byju's Answer
Standard XII
Mathematics
Sum of Trigonometric Ratios in Terms of Their Product
If x + iy =...
Question
If
x
+
i
y
=
1
1
+
C
o
s
θ
+
i
S
i
n
θ
, then show that
4
x
2
−
1
=
0
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Solution
x
+
i
y
=
1
1
+
c
o
s
θ
+
i
s
i
n
θ
=
1
2
c
o
s
2
θ
2
+
i
2
s
i
n
θ
2
.
c
o
s
θ
2
=
1
2
c
o
s
θ
2
×
(
1
c
o
s
θ
2
+
i
s
i
n
θ
2
)
=
0.5
s
e
c
(
θ
2
)
.
1
e
i
θ
2
=
0.5
s
e
c
(
θ
2
)
e
−
i
θ
2
=
0.5
s
e
c
(
θ
2
)
(
c
o
s
θ
2
−
i
s
i
n
θ
2
)
=
0.5
−
i
0.5
t
a
n
θ
2
Hence
x
+
i
y
=
0.5
−
i
0.5
t
a
n
θ
2
Therefore
x
=
0.5
=
1
2
Or
2
x
=
1
Or
4
x
2
=
1
or
4
x
2
−
1
=
0
.
Hence proved.
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Sum of Trigonometric Ratios in Terms of Their Product
Standard XII Mathematics
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