Question

Trigonometric identities

Answer 1

answer B:

`x= (\pi)/(2)\ or\ (\pi)/(6)\ or\ x=(5\pi)/(6)`

Explanation:

`2cos^2 x + 3sin x=3\\\\\Longrightarrow\ 2*(1-sin^2 x)+3sin x -3=0\\\\\Longrightarrow\ 2-2sin^2 x+3 sin x -3=0\\\\\Longrightarrow\ -2sin^2 x+3 sin x -1=0\\\\\Longrightarrow\ 2sin^2 x-3 sin x +1=0\\\\\Delta=3^2-4*2*1=1\\\\sin\ x=(3-1)/(4) \ or\ sin\ x=(3+1)/(4)\\\\sin\ x=(1)/(2) \ or\ sin\ x=1\\\\\Longrightarrow\ x= (\pi)/(6)\ or\ x= (5\pi)/(6)\ or\ x=(\pi)/(2) \\`