(3)四條sin cos tan

10
(sin^2 θ) / (1+ 2cos^2 θ) = (3/19)
sin^2 θ= (1+ 2cos^2 θ) (3/19)
sin^2θ= [(1+ 2(1-sin^2 θ)] (3/19)
19sin^2θ= [(9 -6sin^2 θ)]
sin θ=-3/5
cosθ=-4/5
NOW
(tanθ /(1+sec θ )
=(sin θ/cos θ)/[(cos θ+1)/cos θ]
=sin θ/(cos θ+1)
=-3/5/[-4/5+1]
=-3
11
sec θ (sec θ - tan θ ) = x
sec ^2θ -secθtan θ = x
(1-sinθ)/cos^2θ=x
1-sinθ=x(1-sin^2θ)
x=(1-sinθ)/(1-sin^2θ)
x=1+sinθ
sinθ=x-1

12
2cosx - cotx = 0
2cosx = cotx
2cosx = cosx/sinx
2sinxcosx-cosx=0
cosx(2sinx-1)=0
cosx=0 or sinx=1/2
when cosx=0
x=90, 270
when sinx=1/2
x=30, 150
13
tan^4 θ + 4sec^2 θ - 9 = 0
tan^4 θ+ 4(1+ tan^2θ) - 9 = 0
tan^4 θ+ 4 tan^2θ - 5 = 0
(tan^2 θ+5)(tan^2 θ-1)=0
tan^2 θ=-5 (rejected) or tan^2 θ=1
when tan^2 θ=1
tan^2 θ-1=0
(tan θ+1)(tan θ-1)=0
tan θ=1 or -1
θ=45, 135, 225 , 315