Question

Prove that sintheta+1-costheta/costheta-1+sintheta=1+sintheta/costheta

Answer 1

Step-by-step explanation:

let theta be A (this is for easy to write)

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

{sinA+(1-cosA)}²/(sinA)²-(1-cosA)²

sin²A+2sinA-2sinAcosA+(1-2cosA+cos²A)/sin²A-(1-2cosA+cos²A)

sin²A+cos²A+1+2sinA-2sinAcosA-2cosA/sin²A-1+2cosA-cos²A

(2+2sinA)-(2sinAcosA+2cosA)/1-cos²A-1+2cosA-cos²A

2(1+sinA)-2cosA(1+sinA)/2cosA-2cos²A

(2-2cosA)(1+sinA)/cosA(2-2cosA)

1+sinA/cosA

L.H.S= R.H.S