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Standard XII
Mathematics
Question
If
3
sin
θ
+
5
cos
θ
=
5
then
5
sin
θ
−
3
cos
θ
=
±
2
±
3
±
4
±
5
A
±
2
B
±
5
C
±
3
D
±
4
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Solution
Verified by Toppr
The correct option is
B
±
3
Let
5
sin
θ
−
3
cos
θ
=
x
Then
(
3
sin
θ
+
5
cos
θ
)
2
+
(
5
sin
θ
−
3
cos
θ
)
2
=
9
(
sin
2
θ
+
cos
2
θ
)
+
25
(
cos
2
θ
+
sin
2
θ
)
=9+25=34
∴
x
2
+
25
=
34
o
r
x
2
=
9
o
r
x
=
±
3
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