Question

Simplify `cosx+sinx/cotx`?

Answer 1

Please see below.

Explanation:

`cosx+sinx/cotx`

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

= `cosx+sinx×sinx/cosx`

= `cosx+sin^2x/cosx`

= `(cos^2x+sin^2x)/cosx`

= `1/cosx`

= `secx`

Answer 2

`"see explanation"`

Explanation:

`"using the "color(blue)"trigonometric identities"`

`•color(white)(x)cotx=cosx/sinx`

`•color(white)(x)secx=1/cosx`

`•color(white)(x)cos^2x+sin^2x=1`

`"consider the left hand side"`

`cosx+sinx/cotx`

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

`=cosx+sinx/1xxsinx/cosx`

`=(cos^2x+sin^2x)/cosxlarrcolor(blue)"LCD of cosx"`

`=1/cosx`

`=secx=" right hand side "rArr"verified"`