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CDS Model Paper 4 Mathematics
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© examsnet.com
Question : 44
Total: 100
If
a
cos
θ
+
b
sin
θ
=
m
and
a
sin
θ
−
b
cos
θ
=
n
, then
a
2
+
b
2
=
m
2
−
n
2
m
2
n
2
n
2
−
m
2
m
2
+
n
2
Validate
Solution:
(
a
cos
θ
+
b
sin
θ
)
2
+
(
a
sin
θ
−
b
cos
θ
)
2
=
m
2
+
n
2
a
2
cos
2
θ
+
b
2
sin
2
θ
+
2
a
b
cos
θ
.
sin
θ
+
a
2
sin
2
θ
+
b
2
cos
2
θ
−
2
a
b
sin
θ
.
cos
θ
=
m
2
+
n
2
or
a
2
(
cos
2
θ
+
sin
2
θ
)
+
b
2
(
sin
2
θ
+
cos
2
θ
)
=
m
2
+
n
2
or
a
2
+
b
2
=
m
2
+
n
2
© examsnet.com
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