Find exact solutions of the equation a 2sin2x 3sinx 1 b Sol

Find exact solutions of the equation: a) 2sin^2x + 3sinx+ 1 b) Solve: sec x csc x = 2 csc x Solve:a) 2sin^2x + 3 cosx - 3=0 b) Solve: 3tan x/2 + 3 c) Use the half-angle formula to determine the exact value for sine and cosine of 67 degree 30\' Verify: a) tanx + cos x/1 + sin x b) cos theta cot theta/1 - sin theta - 1 = csc theta

Solution

4. 2 sin^2 x +3sinx +1=0

(2sin x+1)(sin x+1)=0

Sinx=-1/2 sin x=-1

x= sin^-1-1/2 x=sin^-1-1

x=-pi/6, -pi/2

b. sec x cscx = 2csc x

cscx(secx -2)=0

cscx=0 secx=2

X=0 x=pi/3