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The slope of the tangent to the curve ...

The slope of the tangent to the curve
`y=ln(cosx)" at "x=(3pi)/(4)" is "`

A

1

B

`-1`

C

`l n sqrt2`

D

` (1)/(sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`y=l n(cos x)`
Let `t= cos x to (dt)/(dx)=-sin x`
so `y =kl nt `
`(dy)/(dx) =1/t. (dt)/(dx)`
`(dy)/(dx) =(1)/(cosx)xx(-sin x)`
`=-tan x`
`at x=(3pi)/(4)`
`((dy)/(dx))_(x =3pi//4)=-tan 3pi//4=1`
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