Question

Prove that (1+cot A - cosec A) (1+tan A+sec A)=2 ​

Answer 1

Step-by-step explanation:

Given L.H.S

(1+cotA -cosecA)(1+ tan A +sec A ) =2

:- cotA = cosA/sinA

:- tan A = sinA/cosA

:- cosecA =1/sinA

:- sec A =1/cosA

now put

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

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

{(sinA+cosA)²-1}/sinAcosA

{ sin²A+cos²A +2sinAcosA -1}/ sinA.cosA

As we know sin²A + cos²A =1

{1+2sinAcosA -1}/sinA.cosA

= 2sinA.cosA/sinA.cosA

hope it helped you Thanku