F4 maths

1.
log3/log x+log9/log x=3
log(9x3)/logx=3
log27=3logx
27=x^3
x=3

2.
sinθtanθ+cosθ-2sinθ=0
sinθ (sinθ /cosθ)+cosθ-2sinθ=0
sin^(2)θ +cos^(2)θ-2sinθcosθ =0
( sinθ -cosθ )^(2) =0
sinθ-cosθ=0
sinθ=cosθ
( sinθ)/(cosθ )=0
tan θ=1
θ = 45(degree) or 225(degree)

1.
log3/logx + log9/logx = 3
log3 + 2log3 = 3logx
3log3 = 3logx
x = 3

2. Assume the angle is from 0=< θ =< 360 (degree)
sinθtanθ+cosθ-2sinθ=0
tanθ + cotθ -2 = 0 [note: cotθ = cosθ / sinθ]
sin^2(θ) + cos^2(θ) = 2(sinθcosθ) ---------- (*)
sin^2(θ) -2sinθcosθ+ cos^2(θ) = 0
(sinθ - cosθ)^2 = 0
sinθ = cosθ
tanθ = 1
θ = 45(degree) or 225(degree)

Another method: (using the formula : sin(2θ)=2sinθcosθ )

At * : sin^2(θ) +cos^2(θ) = 2sinθcosθ
1 = sin(2θ)
2θ = 90(degree) or 450(degree) 0 =< 2θ =< 720 (degree)
θ = 45(degree) or 225(degree)