中二ge數學題

first prove the formula sin2θ=2sinθcosθ
by using sin(a+b)=sin a cos b + cos a sin b

sin2θ =sin(θ+θ)
=sinθcosθ+cosθsinθ
2sinθcosθ

as sinθcosθ=1/4
2sinθcosθ=1/2
sin(2θ)=1/2
2θ= 180k deg + (-1)^k * 30deg
θ=90k+(-1)^k*15 deg
for principle value (i.e. -180<θ<180)
θ= 15 deg, 75 deg, -105 deg & -165 deg

actually this should not be a question for Form 2 student, it should be at least for cert level.