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Byju's Answer
Standard XII
Mathematics
Differentiation Using Substitution
If 3 sin x+4 ...
Question
If 3 sin x + 4 cos x = 5, then 4 sin x − 3 cos x =
(a) 0
(b) 5
(c) 1
(d) None of these
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Solution
(a) 0
3
sin
x
+
4
cos
x
=
5
3
5
sin
x
+
4
5
cos
x
=
1
Let
cos
α
=
3
5
and
sin
α
=
4
5
.
∴
cos
α
sin
x
+
sinαcos
x
=
1
⇒
sin
α
+
x
=
sin
π
2
⇒
α
+
x
=
π
2
⇒
x
=
π
2
-
α
.
.
.
.
(
1
)
We
have
to
find
the
value
of
4
sin
x
-
3
cos
x
.
4
sin
π
2
-
α
-
3
cos
π
2
-
α
.
.
.
{
From
eq
(
1
)
}
=
4
cos
α
-
3
sinα
=
4
×
3
5
-
3
×
4
5
∵
cos
α
=
3
5
and
sin
α
=
4
5
=
0
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7
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