1/3+2sinx-cosx . evaluate the question
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1
Answer:
Let
∫
3+2sinx+cosx
dx
Put
tan(
2
x
)=
t
∴ x= 2tan
−1
t
∴ dx=
1+t
2
2dt
and
sinx=
1+t
2
2t
,cosx=
1 + t 2
1 − t 2
∴ I= ∫
3+2 (
1+t
2
2t
) + (
1+t
2
1−t
2
)
1
.
1+t
2
2dt
= ∫
3(1+t
2
)+4t+(1−t
2
)
1+t
2
.
1+t
2
2dt
= 2∫
2t
2
+4t+4
dt
= ∫
t 2
dt
= ∫
(t
2
+2t+1)+1
dt
= ∫
(t+1)
2
+1
2
dt
=
1
1
tan
−1
(
1
t+1
) +
c
=
tan
−1
[tan (
2
x
) +1]
+
Explanation:
Hi !!
Hope it helps you !!
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