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Byju's Answer
Standard XII
Mathematics
Implicit Differentiation
7)Prove that ...
Question
7)Prove that Cos 2π/3 cos π/3 – Sin 2π/3 sin π/3 = -(√3+1)/2√2
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Solution
Note: In your question R.H.S. should be -1 instead of -(√3+1)/2√2 .
L
.
H
.
S
.
=
cos
2
π
3
cos
π
3
-
sin
2
π
3
sin
π
3
=
cos
2
π
3
+
π
3
Using
the
formula
,
cosAcosB
-
sinAsinB
=
cos
A
+
B
=
cos
3
π
3
=
cos
π
=
-
1
=
R
.
H
.
S
.
Hence
Proved
.
Suggest Corrections
0
Similar questions
Q.
sin
−
1
x
−
sin
−
1
y
=
2
π
3
;
cos
−
1
x
−
cos
−
1
=
π
3
.
Q.
If
s
i
n
−
1
x
+
s
i
n
−
1
y
=
2
π
3
c
o
s
−
1
x
−
c
o
s
−
1
y
=
π
3
, then
Q.
Solve for
x
and
y
;
sin
−
1
x
+
sin
−
1
y
=
2
π
3
and
cos
−
1
x
−
cos
−
1
y
=
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.
The number of solution(s) of
(
x
,
y
)
so that
sin
−
1
x
+
sin
−
1
y
=
2
π
3
,
cos
−
1
x
−
cos
−
1
y
=
π
3
is
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