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Byju's Answer
Standard XII
Mathematics
Properties Derived from Trigonometric Identities
Find the valu...
Question
Find the value of
cos
−
1
(
cos
2
π
3
)
+
sin
−
1
(
sin
2
π
3
)
.
Open in App
Solution
Given,
cos
−
1
(
cos
2
π
3
)
+
sin
−
1
(
sin
2
π
3
)
=
cos
−
1
(
cos
(
π
−
π
3
)
)
+
sin
−
1
(
sin
(
π
−
π
3
)
)
=
cos
−
1
(
−
cos
(
π
3
)
)
+
sin
−
1
(
sin
π
3
)
=
cos
−
1
(
−
1
2
)
+
sin
−
1
(
√
3
2
)
=
π
−
π
3
+
π
3
=
π
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0
Similar questions
Q.
The principle value of
cos
−
1
(
cos
2
π
3
)
+
sin
−
1
(
sin
2
π
3
)
is:
Q.
What is the principal value of
cos
−
1
(
cos
2
π
3
)
+
sin
−
1
(
sin
2
π
3
)
Q.
Using principal values, evaluate the following
cos
−
1
(
cos
2
π
3
)
+
sin
−
1
(
sin
2
π
3
)
Q.
Consider the following statement :
(i)
s
i
n
−
1
(
s
i
n
2
π
3
)
=
2
π
3
(ii)
t
a
n
−
1
(
t
a
n
2
π
3
)
=
−
π
3
(iii)
c
o
s
−
1
(
c
o
s
2
π
3
)
=
2
π
3
(iv)
s
e
c
−
1
(
s
e
c
5
π
4
)
=
3
π
4
Q.
Consider the following statement :
(i)
s
i
n
−
1
(
s
i
n
2
π
3
)
=
2
π
3
(ii)
t
a
n
−
1
(
t
a
n
2
π
3
)
=
−
π
3
(iii)
c
o
s
−
1
(
c
o
s
2
π
3
)
=
2
π
3
(iv)
s
e
c
−
1
(
s
e
c
5
π
4
)
=
3
π
4
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