Question

Prove that `tanx+cotx/cscx=1/cosx`?

Answer 1

Please see below.

Explanation:

`tanx+cotx/cscx`

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

= `sinx/cosx+cosx/sinx xxsinx`

= `sinx/cosx+cosx`

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

= `(sqrt(1-cos^2x)+cos^2x)/cosx`

If it is, however, `(tanx+cotx)/cscx`

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

= `(sin^2x+cos^2x)/(sinxcosx)xxsinx`

= `1/(cancelsinxcosx)xxcancelsinx`

= `1/cosx`