sin (a+b).sin (a-b)=......................?
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Answer:
The standard formula for
sin
(
A
+
B
)
is:
sin
(
A
+
B
)
=
sin
(
A
)
cos
(
B
)
+
cos
(
A
)
sin
(
B
)
Now
sin
(
−
B
)
=
−
sin
(
B
)
and
cos
(
−
B
)
=
cos
(
B
)
, so
sin
(
A
−
B
)
=
sin
(
A
)
cos
(
B
)
−
cos
(
A
)
sin
(
B
)
So:
sin
(
A
+
B
)
⋅
sin
(
A
−
B
)
=
(
sin
A
cos
B
+
cos
A
sin
B
)
(
sin
A
cos
B
−
cos
A
sin
B
)
=
(
sin
A
cos
B
)
2
−
(
cos
A
sin
B
)
2
...using the identity
(
p
+
q
)
(
p
−
q
)
=
p
2
−
q
2
.
=
sin
2
A
cos
2
B
−
sin
2
B
cos
2
A
=
sin
2
A
(
1
−
sin
2
B
)
−
sin
2
B
(
1
−
sin
2
A
)
...using
sin
2
θ
+
cos
2
θ
=
1
(Pythagoras)
=
sin
2
A
−
sin
2
B
−
sin
2
A
sin
2
B
+
sin
2
B
sin
2
A
=
sin
2
A
−
sin
2
B
I HOPE IT HELP YOU..
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