If sin(a+b)= 2cos(a-b) show that tana=(2-tana)÷(1-2tana)

Question



Answer 1

we can show

tanb = (2-tana)/(1-2tana)

sinacosb+sinbcosa=2cosacosb+2sinasinb (expanding(sin(a+b) and cos(a-b)

cosb(sina-2cosa)=sinb(2sina-cosa) rearranging

cosb(tana-2)=sinb(2tana-1) divide both sides of equation by cosa

tanb = (2-tana)/(1-2tana) divide by cosb, and divide by (1-2tana)