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Byju's Answer
Standard XII
Mathematics
Sign of Trigonometric Ratios in Different Quadrants
Let fz = si...
Question
Let
f
(
z
)
=
s
i
n
z
and
g
(
z
)
=
c
o
s
z
. If * denotes a composition of function then show that
(
f
+
i
g
)
∗
(
f
−
i
g
)
=
i
e
−
e
i
z
.
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Solution
(
f
−
i
g
)
(
z
)
=
f
(
z
)
−
i
g
(
z
)
=
s
i
n
z
−
i
c
o
s
z
=
−
i
(
c
o
s
z
+
s
i
n
z
)
=
−
i
e
i
z
∴
(
f
+
i
g
)
∗
(
f
−
i
g
)
(
z
)
=
(
f
+
i
g
)
(
−
i
e
i
z
)
=
f
(
−
i
e
i
z
)
+
i
g
(
−
i
e
i
z
)
=
s
i
n
(
−
i
e
i
z
)
+
i
c
o
s
(
−
e
i
z
)
=
i
e
−
i
(
−
i
e
i
z
)
=
i
e
−
e
i
z
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0
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