Question

If 3 cos2A - sinA = 2, A belongs to [-pie/2 , pie/2]. find A

Answer 1

Answer:

1/3

Step-by-step explanation:

3(1-2sin^2 A) - sin A = 2 ( cos 2A = 1-2sin^2 A)

3 - 6 sin^2 A - sin A - 2 = 0

6sin^2 A + sin A -1 = 0

put sin A = x

then

6x^2 + x -1 =0

6x^2 +3x-2z -1=0

3x(2x+1)-1(2x+1)=0

(3x-1)(2x+1)=0

3x-1=0. or 2x+1=0

x=1/3 or x= -1/2

then sin A = 1/3 or Sin A = -1/2

given that A lines in 1st quardent

sin A = 1/3 or Sin A = -1/2

A = -sin ^-1 (1/2)

A = - sin^-1 ( sin pie/6)

A = - pie/6