Understanding Engineering Mathematics

(iv) −

1

2

cos 2x+

1

2

(

cos 2− 1

sin 2

)

sin 2x+

1

2

(v)

2

9

[

e^3 − 1

e^6 − 1

]

e^3 x+

2

9

e^3

[

e^3 − 1

e^6 − 1

]

e−^3 x−

2

9

=

2

9 (e^2 + 1 )

e^3 x+

2 e^3

9 (e^3 + 1 )

e−^3 x−

2

9

(vi) −2cosx+

2 (cos 1− 1 )

sin 1

sinx+ 2