sin theta(1 + tan theta) + cos theta(1 + cot theta) = sec theta + cosec theta
plzz complete it as i am new to this chapter
sinx(1+tanx)+cosx(1+cotx)
=sinx(1+tanx)+cosx[(1+tanx)/tanx]............................ [cotx=1/tanx]
=(1+tanx)[sinx+(cosx/tanx)]
=(1+tanx)[(sinx)^2+(cosx)^2]/sinx............................. [tanx=sinx/cosx]
=(1+tanx)/sinx
=((1/sinx)+(tanx/sinx))
=secx+cosecx