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Mathematics
Mathematics
Problem
If
p
1
,
p
2
p_1, p_2
p
1
,
p
2
denotes the lengths of the perpendiculars from the origin on the lines
x
sec
α
+
y
csc
α
=
2
a
x \sec \alpha + y \csc \alpha = 2a
x
sec
α
+
y
csc
α
=
2
a
and
x
cos
α
+
y
sin
α
=
a
cos
2
α
x \cos \alpha + y \sin \alpha = a \cos 2\alpha
x
cos
α
+
y
sin
α
=
a
cos
2
α
respectively, then
(
p
1
p
2
+
p
2
p
1
)
2
\left(\frac{p_1}{p_2} + \frac{p_2}{p_1}\right)^2
(
p
2
p
1
+
p
1
p
2
)
2
is equal to- (1)
4
sin
2
4
α
4 \sin^2 4\alpha
4
sin
2
4
α
(2)
4
cos
2
4
α
4 \cos^2 4\alpha
4
cos
2
4
α
(3)
4
csc
2
4
α
4 \csc^2 4\alpha
4
csc
2
4
α
(4)
4
sec
2
4
α
4 \sec^2 4\alpha
4
sec
2
4
α
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