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AP EAMCET Engineering 2013 Solved Paper
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© examsnet.com
Question : 103
Total: 160
If
sin
θ
+
cos
θ
=
p
and
sin
3
θ
+
cos
3
θ
=
q
then
p
(
p
2
−
3
)
is equal to
q
2
q
−
q
−
2
q
Validate
Solution:
Given,
sin
θ
+
cos
θ
=
p
.......(i)
and
sin
3
θ
+
cos
3
θ
=
q
.......(ii)
⇒
(
sin
θ
+
cos
θ
)
(
sin
2
θ
−
sin
θ
.
cos
θ
+
cos
2
θ
)
=
q
⇒
p
(
1
−
sin
θ
.
cos
θ
)
=
q
[From Eq. (i) and
sin
2
θ
+
cos
2
θ
=
1
]
⇒
1
−
sin
θ
.
cos
θ
=
q
p
⇒
sin
θ
.
cos
θ
=
1
−
q
p
......(iii)
On squaring both sides of Eq. (i), we get
sin
2
θ
+
cos
2
θ
+
2
sin
θ
.
cos
θ
=
p
2
⇒
1
+
2
(
1
−
q
p
)
=
p
2
[from Eq. (iii)]
⇒
p
+
2
(
p
−
q
)
=
p
3
⇒
3
p
−
2
q
=
p
3
⇒
p
3
−
3
p
=
−
2
q
⇒
p
(
p
2
−
3
)
=
−
2
q
© examsnet.com
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