Question

if y=cos^-1(cosx) then dy/dt×atx= 5π/4 is equal to​

Answer 1

Step-by-step explanation:

Given,

y=cos

−1

cosx

dx

dy

=

dx

d

(cos

−1

(cos(x)))

Let f=cos

−1

(u),u=cos(x)

=

du

d

(cos

−1

(u))

dx

d

(cos(x))

=(−

1−u

2

1

)(−sin(x))

=(−

1−cos

2

(x)

1

)(−sin(x))

∴

dx

dy

=

sin

2

(x)

sin(x)

dx

dy

x=

4

5π

=

sin

2

(

4

5π

)

sin(

4

5π

)

=

1−cos(

2

π

)

2

sin(

4

5π

)

=

1−0

2

(−

2

2

)

=−1

hope so it may help you

please follow me

thanks my answer

marked as brainlist

Answer 2

❤Hope it helps u Mark as brainliest if it helps u ❤

y=cos

−1

cosx

dx

dy

=

dx

d

(cos

−1

(cos(x)))

Let f=cos −1 (u),u=cos(x)

= dud (cos

−1 (u)) dxd (cos(x))

=(− 1−u 21 )(−sin(x))

=(− 1−cos 2

(x)

1 )(−sin(x))

∴ dxdy = sin 2 (x)

sin(x)

dxdy

x= 45π

= sin 2 ( 45π )

sin( 45π )

= 1−cos( 2π )2 sin( 45π )

= 1−02

(− 22 )

=−1