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Byju's Answer
Standard XII
Mathematics
General Solution of Trigonometric Equation
If cos A+B ...
Question
If
cos
(
A
+
B
)
cos
(
A
−
B
)
=
sin
(
C
+
D
)
sin
(
C
−
D
)
, prove that
tan
A
tan
B
tan
C
+
tan
D
=
0
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Solution
cos
(
A
+
B
)
cos
(
A
−
B
)
=
sin
(
C
+
D
)
sin
(
C
−
D
)
Using compounds dividend
cos
(
A
+
B
)
+
cos
(
A
−
B
)
cos
(
A
+
B
)
−
cos
(
A
−
B
)
=
sin
(
C
+
D
)
+
sin
(
C
−
D
)
sin
(
C
+
D
)
−
sin
(
C
−
D
)
2
cos
A
⋅
cos
B
−
2
sin
A
⋅
sin
B
=
2
sin
C
⋅
cos
D
2
cos
C
⋅
sin
D
−
cot
A
⋅
cot
B
=
tan
C
⋅
cot
D
−
1
tan
A
⋅
tan
B
=
tan
C
tan
D
∴
−
tan
D
=
tan
A
⋅
tan
B
⋅
tan
C
∴
tan
A
⋅
tan
B
⋅
tan
C
+
tan
D
=
0
.
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Similar questions
Q.
If cos (A + B) sin (C − D) = cos (A − B) sin (C + D), prove that tan A tan B tan C + tan D = 0.
Q.
If
cos
(
A
−
B
)
cos
(
A
+
B
)
+
cos
(
C
+
D
)
cos
(
C
−
D
)
=
0
, then
tan
A
t
a
n
B
tan
C
=
Q.
If
cos
(
A
+
B
)
sin
(
C
−
D
)
=
cos
(
A
−
B
)
sin
(
C
+
D
)
,
then the value of
tan
A
tan
B
tan
C
+
tan
D
is
Q.
In any quadrilateral
A
B
C
D
, prove that
(i)
sin
(
A
+
B
)
+
sin
(
C
+
D
)
=
0
(ii)
cos
(
A
+
B
)
=
cos
(
C
+
D
)
.
Q.
In cyclic quadrilateral
A
B
C
D
, prove that
i .
sin
(
A
+
B
)
+
sin
(
C
+
D
)
=
0
ii.
cos
(
A
+
B
)
=
cos
(
C
+
D
)
.
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