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Byju's Answer
Standard XII
Mathematics
Basic Inverse Trigonometric Functions
If sin alp...
Question
If sin α − sin β = a and cos α + cos β = b, then write the value of cos (α + β).
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Solution
cos
(
α
+
β
)
=
cos
α
cos
β
-
sin
α
sin
β
=
2
cos
α
cos
β
-
2
sin
α
sin
β
+
2
-
2
2
=
sin
2
α
+
cos
2
α
+
sin
2
β
+
cos
2
β
+
2
cos
α
cos
β
-
2
sin
α
sin
β
-
2
2
=
(
s
i
n
α
-
s
in
β
)
2
+
(
cos
α
+
cos
β
)
2
-
2
2
=
a
2
+
b
2
-
2
2
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0
Similar questions
Q.
If
α
and
β
are complementary angle such that qsin
α
= P , then find the value of
(
sin
α
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β
−
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sin
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)
Q.
If
β
and
α
are +ive angles less than two right angles and
c
o
s
α
+
c
o
s
(
α
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β
)
+
c
o
s
(
α
+
β
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γ
)
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s
i
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α
+
s
i
n
(
α
+
β
)
+
s
i
n
(
α
+
β
+
γ
)
=
0
then
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=
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=
2
π
/
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Q.
Let
α
and
β
be such that
π
<
α
−
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<
2
π
. If
sin
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+
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β
=
−
21
65
and
cos
α
+
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β
=
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, then the value of
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−
β
2
is
Q.
Prove that if
α
,
β
, and
γ
are angles of a triangle, then sin
α
×
s
i
n
β
−
c
o
s
γ
=
c
o
s
α
c
o
s
β
Q.
L
e
t
α
,
β
b
e
s
u
c
h
t
h
a
t
π
<
α
−
β
<
3
π
.
I
f
s
i
n
α
+
s
i
n
β
=
21
65
a
n
d
c
o
s
α
+
c
o
s
β
=
−
27
65
,
t
h
e
n
t
h
e
v
a
l
u
e
o
f
c
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s
α
−
β
2
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s
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