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Byju's Answer
Standard XII
Mathematics
Inverse of a Function
If x and ...
Question
If
x
and
y
are acute angles such that
cos
x
=
13
14
and
cos
y
=
1
7
prove that
(
x
−
y
)
=
−
π
3
,
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Solution
given,
cos
x
=
13
14
cos
y
=
1
y
∵
x
&
y
are acute angles
∴
sin
x
=
√
1
−
cos
2
x
=
√
1
−
169
196
=
√
27
196
sin
x
=
3
√
3
14
and
sin
y
=
√
1
−
cos
2
y
=
√
1
−
1
49
=
√
48
49
sin
y
=
4
√
3
7
Now
cos
(
x
−
y
)
=
csc
x
cos
y
+
sin
x
sin
y
=
13
14
×
1
7
+
3
√
3
14
×
4
√
3
7
=
13
+
36
14
×
7
=
49
14
×
7
=
1
2
∴
|
x
−
y
|
=
cos
−
1
1
2
=
π
3
⇒
|
x
−
y
|
=
π
3
−
−
−
−
−
(
1
)
Now, we know
cos
θ
is a decreasing function
and
13
14
>
1
7
⇒
cos
x
>
cos
y
⇒
x
<
y
⇒
x
−
y
<
0
from
(
1
)
∴
−
(
x
−
y
)
=
π
3
⇒
x
−
y
=
−
π
3
Proved
Suggest Corrections
0
Similar questions
Q.
If
x
and
y
are acute angles such that
cos
x
+
cos
y
=
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2
and
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+
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then
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Q.
In
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, if
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are acute angles such that
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y
and
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y
satisfy the equation
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0
, then
Q.
If
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such that
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