Question

(ix) integrate cos X - sin x (2 + 2 sin 2x) cos x + sin x​

Answer 1

Step-by-step explanation:

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∫

cosx+sinx

cosx−sinx

⋅(2+2sin

2

xdx)

⇒2×∫

(cosx+sinx)

cosx−sinx

(sin

2

x+cos

2

xsin

2

x)dx

⇒2∫

cosx+sinx

cosx−sinx

×[sinx+cosx]

2

dx

⇒2∫(cosx−sinx)(cosx+sinx)dx

⇒2∫cos

2

x−sin

2

xdx

⇒2×∫cos

2

xdx

⇒2×

2

sin

2

x

+c

⇒sin

2

x+cAns.