Question

Question #2b836

Answer 1

Please see below.

Explanation:

`(secx+tanx)cosx-1=sinx`

`secx=1/cosx`

and `tanx=sinx/cosx`

Let's plug them in:

`(1/cosx+sinx/cosx)cosx-1=sinx`

`(cosx/cosx+(sinxcosx)/cosx)-1=sinx`

`1+sinx-1=sinx`

`sinx=sinx`

So, this equation holds true for all values of `x`.

But we can do it also by plugging in `pi/3` for `x`:

`(sec(pi/3)+tan(pi/3))cos(pi/3)-1=sin(pi/3)`

`(2+sqrt3)(1/2)-1=sqrt3/2`

`1+sqrt3/2-1=sqrt3/2`

`sqrt3/2=sqrt3/2`