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CBSE
MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals
Problem
∫
d
x
cos
x
−
sin
x
\int \frac{dx}{\cos x - \sin x}
∫
c
o
s
x
−
s
i
n
x
d
x
is equal to (a)
1
2
log
∣
tan
(
x
2
+
3
π
8
)
∣
+
c
\frac{1}{\sqrt{2}} \log \left| \tan \left( \frac{x}{2} + \frac{3\pi}{8} \right) \right| + c
2
1
lo
g
tan
(
2
x
+
8
3
π
)
+
c
(b)
1
2
log
∣
cot
(
x
2
)
∣
+
c
\frac{1}{\sqrt{2}} \log \left| \cot \left( \frac{x}{2} \right) \right| + c
2
1
lo
g
cot
(
2
x
)
+
c
(c)
1
2
log
∣
tan
(
x
2
−
3
π
8
)
∣
+
c
\frac{1}{\sqrt{2}} \log \left| \tan \left( \frac{x}{2} - \frac{3\pi}{8} \right) \right| + c
2
1
lo
g
tan
(
2
x
−
8
3
π
)
+
c
(d)
1
2
log
∣
tan
(
x
2
−
π
8
)
∣
+
c
\frac{1}{\sqrt{2}} \log \left| \tan \left( \frac{x}{2} - \frac{\pi}{8} \right) \right| + c
2
1
lo
g
tan
(
2
x
−
8
π
)
+
c
Related theory
Integration Techniques
Standard trigonometric integrals
Integration using trigonometric identities
Integrals
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