Question

Question #1f5ff

Answer 1

Let us start with the LHS:

`LHS = ((sintheta+costheta)/sintheta)-((costheta-sintheta)/costheta)`

`" " = ((sintheta+costheta)costheta-(costheta-sintheta)sintheta)/(sinthetacostheta)`

`" " = ((sinthetacostheta+cos^2theta)-(costhetasintheta-sin^2theta))/(sinthetacostheta)`

`" " = (sinthetacostheta+cos^2theta-costhetasintheta+sin^2theta)/(sinthetacostheta)`

`" " = (cos^2theta+sin^2theta)/(sinthetacostheta)`

`" " = (1)/(sinthetacostheta)`

`" " = 1/sintheta*1/costheta`

`" " = csctheta*sectheta`

`" " = RHS \ \ \ \ ` QED

Answer 2

`LHS=(sintheta+costheta)/sintheta-(costheta-sintheta)/costheta`

`=sintheta/sintheta+costheta/sintheta-costheta/costheta+sintheta/costheta`

`=cancel1+costheta/sintheta-cancel1+sintheta/costheta`

`=(cos^2theta+sin^2theta)/(sinthetacostheta)`

`=1/(sinthetacostheta)`

`=secthetacsctheta=RHS`