Question

Prove that:
(cosA/1+cosA)+(1+sinA/cosA)

Answer 1

Answer:

Step-by-step explanation:

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

Dividing in Nr and Dr by cosA

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

=[secA+tanA+1]/[secA-tanA+1]. , [putting 1=sec^2A-tan^2A=(secA+tanA)(secA-

tanA) in Nr.]

=[(secA+tanA)+(secA+tanA)(secA-tanA)]/[secA-tanA+1].

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

= secA + tanA

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

=(1+sinA)/cosA

Multiplying in Nr and Dr by (1-sinA)

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

=(1-sin^2A)/cosA.(1-sinA)

= cos^2A/cosA.(1-sinA)

= cosA/(1-sinA). Proved.