Precalculus question See photo for question it wouldnt let m

Precalculus question: See photo for question (it wouldn\'t let me post it up here). Please Show all work and if useing a photo make sure its a clear photo and not blurry!

Solution

2cosx+5sinx=4

divide by [2²+5²] =29 on both sides

(2/29 )cosx+(5/29)sinx=4/29

sin(a)cos(b)+cos(a)sin(b)=sin(a+b)

sin(sin^-1(2/29 ) +x) =(4/29)

(sin^-1(2/29 ) +x) =sin^-1(4/29) ,(sin^-1(2/29 ) +x) =-sin^-1(4/29)

x=sin^-1(4/29) -sin^-1(2/29) , x =-sin^-1(4/29) -sin^-1(2/29 )

x=0.4567,x=1.924