Question

(1+cot A -cosec A)(1+tan A+sec A)=2
prove that LHS=RHS

Answer 1

Answer:

LHS=(1+(cos A/sin A)-(1/sinA))(1+(sinA/cosA)+(1/cosA))

       =(1+(cosA-1)/sinA)(1+(sinA+1)/cosA)

       =((sinA+cosA-1)/sinA)((sinA+cosA+1)/cosA

       =((sinA+cosA)^2 -1)/sinA*cosA

       =(sin^2A+cos^2A+2sinAcosA-1)/sinAcosA

       =(1+2sinAcosA-1)/sinAcosA

       =(2sinAcosA)/(sinAcosA)

       =2

hence Proved