F4 Maths question

Simplify
1 Sin(180度+x/2)=－Sin(x/2)
2 Cos(90度-2x)=Sin(2x)
3 Tan (180度+3x)=Tan(3x)
4 Tan (360度-x/3)=－Tan(x/3)

5.When 3(x^2)+px－1is divided by x－2a，the reminder is 15．When p(x^2)+5x－4
is divided by 2x+a，the remainder is －6．Find a and p
Sol
3(2a)^2+p*(2a)－1=15
12a^2+2ap=16
ap=8－6a^2
p(－a/2)^2+5*(－a/2)－4=－6
pa^2－10a=－8
a(8－6a^2)－10a=－8
－6a^3－2a+8=0
3a^3+a－4=0
(3a^2+3a+4)(a－1)=0
Since 3a^2+3a+4>0 (D=9－4*3*4<0)
So
a=1
p=2