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Byju's Answer
Standard XII
Mathematics
Substitution Method to Remove Indeterminate Form
Show that s...
Question
Show that
sin
(
x
+
y
)
sin
(
x
−
y
)
=
tan
x
+
tan
y
tan
x
−
tan
y
Open in App
Solution
RHS
tan
x
+
tan
y
tan
x
−
tan
y
=
sin
x
cos
x
+
sin
y
cos
y
sin
x
cos
x
−
sin
y
cos
y
=
sin
x
cos
y
+
sin
y
cos
x
cos
x
cos
y
sin
x
cos
y
−
sin
y
cos
x
cos
x
cos
y
=
sin
x
cos
y
+
sin
y
cos
x
sin
x
cos
y
−
sin
y
cos
x
=
sin
(
x
+
y
)
sin
(
x
−
y
)
Hence proved.
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3
Similar questions
Q.
Prove that:
sin
(
x
+
y
)
sin
(
x
−
y
)
=
tan
x
+
tan
y
tan
x
−
tan
y
Q.
If
s
i
n
(
x
+
y
)
s
i
n
(
x
−
y
)
=
a
+
b
a
−
b
,
Show that
t
a
n
x
t
a
n
y
=
a
b
.
Q.
If
s
i
n
(
x
+
y
)
s
i
n
(
x
−
y
)
=
a
+
b
a
−
b
, then
t
a
n
x
t
a
n
y
=
Q.
If
cos
x
=
tan
y
,
cot
y
=
tan
z
and
cot
z
=
tan
x
; then
sin
x
=
Q.
If
sin
(
x
+
y
)
sin
(
x
−
y
)
=
a
+
b
a
−
b
, then the value of
tan
x
tan
y
equals
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