Question

If 4sinAcosA=1-2sinA+2cosA find the value of A ?

Answer 1

`A = pi/6 + 2pin, (5pi)/6 + 2pin, (2pi)/3 + 2pin, (4pi)/3 + 2pin`

Explanation:

This problem is all about factoring. Make sure that you know how to factor!!

`4sinAcosA + 2sinA = 2cosA + 1`

`2sinA(2cosA + 1) = 2cosA + 1`

`2sinA(2cosA + 1) - (2cosA + 1) = 0`

`(2sinA - 1)(2cosA+ 1) = 0`

`sinA = 1/2 or cosA = -1/2`

`A = pi/6 + 2pin, (5pi)/6 + 2pin, (2pi)/3 + 2pin, (4pi)/3 + 2pin`

Hopefully this helps!