The smallest positive number for which sin t cos 2t 0 is t

The smallest positive number for which sin t +cos (2t) = 0 is t =

Solution

sint +cos2t =0

sint +(1-2sin²t) =0

2sin²t-sint -1 =0

2sin²t-2sint+sint -1 =0

2sint(sint -1)+1(sint -1)=0

(sint -1)(2sint +1)=0

sint =1 ,sint =-1/2

t = /2 is the smallest positive number for which sint +cos2t =0