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Byju's Answer
Standard XI
Mathematics
Trigonometric Ratios of Allied Angles
Prove the fol...
Question
Prove the following:
c
o
s
(
π
4
−
x
)
c
o
s
(
π
4
−
y
)
−
s
i
n
(
π
4
−
x
)
s
i
n
(
π
4
−
y
)
=
s
i
n
(
x
+
y
)
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Solution
L
H
S
=
c
o
s
(
π
4
−
x
)
c
o
s
(
π
4
−
y
)
−
s
i
n
(
π
4
−
x
)
s
i
n
(
π
4
−
y
)
=
cos
(
π
4
−
x
+
π
4
−
y
)
Using identity
cos
A
cos
B
−
sin
A
sin
B
=
cos
(
A
+
B
)
=
cos
(
π
2
−
(
x
+
y
)
)
=
sin
(
x
+
y
)
=
R
H
S
∴
c
o
s
(
π
4
−
x
)
c
o
s
(
π
4
−
y
)
−
s
i
n
(
π
4
−
x
)
s
i
n
(
π
4
−
y
)
=
sin
(
x
+
y
)
Hence proved
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0
Similar questions
Q.
Prove that
cos
(
π
4
−
x
)
cos
(
π
4
−
y
)
−
sin
(
π
4
−
x
)
sin
(
π
4
−
y
)
=
sin
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+
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)
Q.
cos{π/4 - x}cos{π/4 - y} - sin{π/4 - x}sin{π/4 - y} = sin(x+y)
Q.
simplify the given equation
cos
(
π
4
−
x
)
cos
(
π
4
−
y
)
−
sin
(
π
4
−
x
)
sin
(
π
4
−
y
)
=
sin
(
x
+
y
)
Q.
Find the value of,
cos
(
π
4
−
x
)
cos
(
π
4
−
y
)
−
sin
(
π
4
−
x
)
sin
(
π
4
−
y
)
by using formula,
cos
A
cos
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−
sin
A
sin
B
=
cos
(
A
+
B
)
Q.
Prove the following:
cos
(
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4
−
x
)
⋅
cos
(
π
4
−
y
)
−
sin
(
π
4
−
x
)
⋅
sin
(
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4
−
y
)
=
sin
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