amaths

1
let y=x-15
then 3tan(x-15)=tan(x+15) becomes
3tan(y)=tan(y+30)
3tan(y)=[tan(y)+tan30]/[1-(tany)(tan30)]
3tan(y)=[tan(y)+1/√3]/[1-(tany)(1/√3)]
3tan(y)[1-(tany)(1/√3)]=[tan(y)+1/√3]
3tan(y)-√3tan^2(y)=tan(y)+1/√3
3√3tan(y)-3tan^2(y)=√3tan(y)+1
3tan^2(y)-2√3tan(y)+1=0
(√3tan(y)-1)^2=0
tan(y)=1/√3
y=180°n+30°or 180°n-30°
x-15°=180°n+30°or 180°n-30°
x=180°n+45°or 180°n-15°


2
2sin(x)cos(p-x)
=sin(x+p-x)+sin(x-p+ x)
=sin(2x-p)+sinp

sin(x)+2sin(x)cos(p- X)-sinp=0
sin(2x-p)+sinp-sinp= 0
sin(2x-p)=0
2x-p=180°n
2x=180°n+p
x=90°n+p/2