Question

How do you prove `(sinx+cosx)(Tanx+cotx)=secx+cscx`?

Answer 1

We have:

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

`(sinx + cosx)((sin^2x + cos^2x)/(sinxcosx)) = secx + cscx`

`(sinx +cosx)/(sinxcosx) = secx + cscx`

`sinx/(sinxcosx) + cosx/(sinxcosx) = secx + cscx`

`1/cosx + 1/sinx = secx + cscx`

`secx + cscx = secx + cscx`

`LHS = RHS`

Hopefully this helps!