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UPSC CDS 2 2020 Math Paper
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© examsnet.com
Question : 25
Total: 100
What is the least value of
9
sin
2
θ
+
16
cos
2
θ
?
0
9
16
25
Validate
Solution:
Least value of
9
sin
2
θ
+
16
cos
2
θ
?
⇒
9
sin
2
θ
+
16
cos
2
θ
=
9
sin
2
θ
+
16
(
1
−
sin
2
θ
)
=
9
sin
2
θ
+
16
−
16
sin
2
θ
=
16
−
7
sin
2
θ
We know that maximum value of
sin
2
θ
is 1.
⇒
Least value of
9
sin
2
θ
+
16
cos
2
θ
=
16
−
7
(
1
)
=
9
© examsnet.com
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