Question

Prove this equation ​

Answer 1

(1+Cot A - Cosec A) (1+TanA+SecA)

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

= [(sinA + cosA)^2 - 1] /sinAcosA

= (sinA^2 + cosA^2 + 2sinAcosA - 1)/sinAcosA

= (1-1 + 2sinacosA) /sinAcosA

= 2

Answer 2

Step-by-step explanation:

(1+cotA-cosecA)(1+tanA+secA)

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

=[( sinA+cosA-1)/sinA ]×[(cosA+sinA+1)

/cosA]

=[(sinA+cosA )^2-1]/sinAcosA

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

=(1+2sinAcosA-1)/sinAcosA

2sinAcosA/sinAcosA = 2

hence proved !