Question

cos square(pi by 6 + x by 2) - sin square ( pi by 6 - x by 2) ​

Answer 1

Step-by-step explanation:

Given, f(x)=2sinx+cos2x

On differentiating w.r.t x, we get

f

′

(x)=2cosx−2sin2x

Put f

′

(x)=0

2cosx−4sinxcosx=0

⇒2cosx(1−2sinx)=0

⇒cosx=0,sinx=

2

1

⇒x=

2

π

,x=

6

π

Now f

′′

(x)=2sinx−4cos2x

At x=

2

π

f

′′

(

2

π

)=−2sin(

2

π

)−4cos2(

2

π

)

=2>0., Minima

At x=

6

π

f

′′

(

6

π

)=−2sin(

6

π

)−4cos2(

6

π

)

=−1−2=−3, Maxima