Question

Find the points at which the tangent equations to the graph of the following functions are parallel to the x-axis = cos 2 − 5 cos x

Answer 1

Given:

The function is

`y=cos2x-5cosx`

Required:

To find the points at which the tangent equations to the graph of the following functions are parallel to the x-axis.

Step-by-step explanation:

Differentiate the given function.

`\begin{gathered} (dy)/(dx)=2(-sin2x)-5(-sinx) \\ (dy)/(dx)=-2sin2x+5sinx \end{gathered}`

Given that tangent to the curve is parallel to the x-axis.

So the slope of the tangent = Slope of X-axis

`\begin{gathered} (dy)/(dx)=0 \\ 5sinx-2sin2x=0 \end{gathered}`

Use the identity

`sin2x=2sinxcosx`

Now

`\begin{gathered} 5sinx-2(2sinxcosx)=0 \\ 5sinx-4sinxcosx=0 \end{gathered}`

Take out common sinx

`sinx(5-4cosx)=0`