Question

Prove That :Tan A÷Sec A - 1 + Tan A/Sec A + 1 = 2 Cosec A

Answer 1

tanA/secA-1 + tanA/secA+1 = 2cosecA

Taking L.H.S

tanA/secA-1 + tanA/secA+1

tanA(secA+1) + tanA(secA-1) / (secA-1)(secA+1)

tanA[ (secA-1)+(secA+1) ] / sec^2A-1

tanA[ secA-1+secA+1 ] / tan^2A

secA-1+secA+1 /tanA

secA+secA / tanA

2secA / tanA

2secA × 1/tanA

2secA × cotA

2secA × cosA/sinA

2×1/cosA × cosA/sinA

cosA and cosA will be cancel out

then,
2/sinA
2×1/sinA
2cosecA

Hence proved