Question

Question #a241c

Answer 1

`sinxsecx(cosx+cscx/ sec ^2 x)`

`=sinxsecxcosx+sinxsecxcscx/ sec ^2 x`

`=sinx*1/cosx*cosx+sinx*cscx/ sec x`

`=sinx+1/ sec x`

`=sinx+cosx=RHS`

Answer 2

`"see explanation"`

Explanation:

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

`•color(white)(x)secx=1/cosx" and "cscx=1/sinx`

`"consider the LHS"`

`sinx/cosx(cosx+1/sinx xxcos^2x)`

`=(sinx/cancel(cosx)xxcancel(cosx))+(cancel(sinx)/cancel(cosx)xx(cosxcancel(cosx))/cancel(sinx))`

`=sinx+cosx=RHSrArr"proven"`