If sinx 14 and secy 74 where x and y lie between 0 and pi2

If sin(x) = 1/4 and sec(y) = 7/4, where x and y lie between 0 and pi/2, evaluate sin(x + y). Find a values of x such that sin 2x = sin x and 0 lessthanorequalto x lessthanorequalto 2 pi. (Enter your answers as a comma-separated list.)

Solution

sinx=1/4 here opposite=1 and hypotenuse=4

Therefore adjacent=sqrt(16-1)=sqrt15

cos x= adjacent/hypotenuse=sqrt15/4

sec y=7/4

Therefore cos y=4/7

Here adjacent=4 and hypotenuse=7

Therefore opposite=sqrt(49-16)=sqrt33

sin y= sqrt33/7

sin(x+y)=sinx cosy + cosx siny= (1/4)(4/7)+ (sqrt15 /4)(sqrt 33/7)

                                                 (4+ sqrt495)/28= (4+ 3sqrt55)/28