Question

f(x)= sinx(1+cosx) in (0,π/2)​

Answer 1

Step-by-step explanation:

ANSWER

f(x)=sinx(1+cosx)

f(x)=sinx+

2

1

sin2x

On differentiating w.r.t x, we get

f

′

(x)=cosx+cos2x

Therefore,

cosx+2cos

2

x−1=0

2cos

2

x+cosx−1=0

2cos

2

x+2cosx−cosx−1=0

(2cosx−1)(cosx+1)=0

cosx=−1orcosx=

2

1

Clearlymaximumoccursatx=

3

π

Hence,

optionCiscorrectanswer.

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