Trigonometric equations?

Question

Help help I don't really understand........

Find the solutions of the equations that are in the interval [0,2(pi))

1.) 1- sin t = (sqrt 3) cos t

2.) cos alpha + sin alpha =1

3.)2 tan t- sec^2 t= 0

Answer 1

1)
sqrt( 3)=tan 60=sin60/cos60

cos60-sintcos60=sin60cost

cos60=sintcos60+sin60cost

cos60=sin(60+t)

sin30=sin(60+t)

30=60+t

t=-30=330

2) let alpha=a

cosa+sina=1
cos^2a+sin^2a+sin2a=1
remember
cos^2a+sin^2a=1
and
2sinacosa=sin2a

sin2a=0
2a=0
a=0
2a=180
a=90

3)2tant=1/cos^2t
2 sint/cost * cos^2t=1

sin2t=1
sin2t=sin90
2t=90
t=45