Question

1/3+2sinx-cosx . evaluate the question​

Answer 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:

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