Question

(1+tan(x))* (1+cot(-x))

Answer 1

(1+tan(x))* (1+cot(-x))

= (1 + sinx/cosx)(1 + cosx/sinx)
= [ (cosx + sinx)/cosx][ (sinx + cosx)/sinx]
= (sin^2 x + cos^2 x + 2sinxcosx) / (sinxcosx)
= (1 + 2sinxcosx)/(sinxcos)
= 1/(sinxcosx) + 2
or
= secs cscx + 2