Question

Show that the equation 1+sinxtanx=5cosx can be expressed as 6cos^2-cosx-1=0?

Answer 1

See the proof below

Explanation:

We need

`tanx=sinx/cosx`

`sin^2x-cos^2x=1`

Therefore,

`1+sinxtanx=5cosx`

`1+sinx*sinx/cosx=5cosx`

Multiply by `cosx`

`cosx+sin^2x=5cos^2x`

Replacing `sin^2x` by `1-cos^2x`

`cosx+1-cos^2x=5cos^2x`

`5cos^2x-cos^2x-cosx-1=0`

`6cos^2x-cosx-1=0`

`QED`