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UPSC CDS Math Trigonometric Ratios and Trigonometric Identities Questions
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© examsnet.com
Question : 95
Total: 107
If
sin
x
+
cos
x
=
p
and
sin
3
x
+
cos
3
x
=
q
then what is
p
3
−
3
p
equal to?
[2014 CDS-II]
0
-2q
2q
4q
Validate
Solution:
sin
x
+
cos
x
=
p
⇒
sin
2
x
+
cos
2
x
+
2
sin
x
cos
x
=
p
2
⇒
sin
x
cos
x
=
p
2
−
1
2
.....(1)
p
=
sin
x
+
cos
x
⇒
p
3
=
sin
3
x
+
cos
3
x
+
3
sin
x
cos
x
(
sin
x
+
cos
x
)
⇒
p
3
=
q
+
3
(
p
2
−
1
2
)
p
[Using (1)]
⇒
2
p
3
=
2
q
+
3
p
3
−
3
p
⇒
p
3
−
3
p
=
−
2
q
© examsnet.com
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