Fill `tanA=(.......)/cosA`

Prove that 1/(secA-tanA)-1/(cosA)=1/cosA-1/(secA-tanA) .

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

Prove that (tanA+secA-1)/(tanA-secA+1)=(1+sinA)/(cosA) .

Find the value of (tanA+secA-1)cosA .

Prove that : (secA+tanA)(1-sinA)=cosA

If cosecA=2 , then (1)/(tanA)+(sinA)/(1+cosA)=?

Prove that: cotA/2-tanA/2=(cosA/2)/(sinA/2)-(sinA/2)/(cosA/2) =(cos^(2)A/2-sin^(2)A/2)/(sinA/2cosA/2) =cosA/(1/2.(2sinA/2cosA/2)) =(2cosA)/(sinA)=2cotA = RHS. Hence Proved.

In a triangle ABC , if tanA=2sin2Cand3cosA=2sinBsinC , then C=