Find all values of t in the interval 0 2 pi satisfying the g

Find all values of t in the interval [0, 2 pi] satisfying the given equation. 2 Squareroot 2 sin 2t + Squareroot 2 tan 2t = 0 t =

Solution

2 sqrt2 sin 2t + sqrt2 tan2t=0

tan 2t= sin2t/cos2t

so we get

2sqrt2 sin2t + sqrt2(sin2t/cos2t)=0

sqrt2 sin 2t(2 + sec 2t)=0

sin 2t=0 and 2+ sec2t=0

sin^-1 2t= sin ^-1(0) and sec 2t=-2

2t=0,180,360 and sec^-1 sec 2t= sec^-1(-2)

t=0,90,180 and t= 120,240

t= 0,90,120,180,240