Question

Question #9b18b

Answer 1

Let

`theta/2=75^@`

`=>theta=150^@`

`=>tantheta=tan150^@`

`=>(2tan(theta/2))/(1-tan^2(theta/2))=tan(180-30)^@`

putting `tan(theta/2)=x`

`=>(2x)/(1-x^2)=-tan30^@=-1/sqrt3`

`=>x^2-2sqrt3x-1=0`

`=>x=(2sqrt3+sqrt((2sqrt3)^2-4*1*(-1)))/2`
[Negative root of x neglected as `tan75>0`]

`=>tan(theta/2)=(2sqrt3+sqrt16)/2`

`=>tan75=(2sqrt3+4)/2`

`=>tan75=2+sqrt3`