1.) $\displaystyle tan(x)=1/sqrt(3)$
2.) $\displaystyle sin(x)^2=1/25$
now i know that this is actually $\displaystyle sin(x)=1/5$.
3.) $\displaystyle 2sin(x)cos(x)+sin(x)-2cos(x)-1=0$
(1) $\displaystyle tan30=1/sqrt(3)$
special angles , it is positive so x = 30 , 210
(2) $\displaystyle sin(x)=1/5$
11.54 is the basic angle , X should be in the first and second quadrant as it is positive .
(3)
sin x -1 = 2 cos x - 2 sinx cos x
sin x-1 = 2 cos x ( 1 - sinx )
1 - sinx = - 2 cosX(1-sin x)
1 = -2cos X
cos X = - 1/2
X = 120 and 240
(3)