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∫
(
sin
θ
cos
3
θ
+
sin
3
θ
cos
9
θ
+
sin
9
θ
cos
27
θ
)
d
θ
\int \left( \frac{\sin \theta}{\cos 3\theta} + \frac{\sin 3\theta}{\cos 9\theta} + \frac{\sin 9\theta}{\cos 27\theta} \right) d\theta
∫
(
c
o
s
3
θ
s
i
n
θ
+
c
o
s
9
θ
s
i
n
3
θ
+
c
o
s
27
θ
s
i
n
9
θ
)
d
θ
…
Mathematics
Problem
∫
(
sin
θ
cos
3
θ
+
sin
3
θ
cos
9
θ
+
sin
9
θ
cos
27
θ
)
d
θ
\int \left( \frac{\sin \theta}{\cos 3\theta} + \frac{\sin 3\theta}{\cos 9\theta} + \frac{\sin 9\theta}{\cos 27\theta} \right) d\theta
∫
(
c
o
s
3
θ
s
i
n
θ
+
c
o
s
9
θ
s
i
n
3
θ
+
c
o
s
27
θ
s
i
n
9
θ
)
d
θ
is equal to a.
1
2
log
∣
sec
27
θ
sec
θ
∣
+
C
\frac{1}{2} \log \left| \frac{\sec 27\theta}{\sec \theta} \right| + C
2
1
lo
g
s
e
c
θ
s
e
c
27
θ
+
C
b.
1
2
log
∣
sec
θ
sec
27
θ
∣
+
C
\frac{1}{2} \log \left| \frac{\sec \theta}{\sec 27\theta} \right| + C
2
1
lo
g
s
e
c
27
θ
s
e
c
θ
+
C
c.
1
2
log
∣
sec
27
θ
3
sec
θ
∣
+
C
\frac{1}{2} \log \left| \frac{\sqrt[3]{\sec 27\theta}}{\sec \theta} \right| + C
2
1
lo
g
s
e
c
θ
3
s
e
c
27
θ
+
C
d. None of these
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