Question

find the magnitude of angle A if
2 Sin A cos A - Cos A - Sin A + 1 = 0

Answer 1

2 sin A . cos A - cos A - 2 sin A + 1 = 0
=> 2 sin A * cos A - cos A - 2 sin A + 1 = 0
=> cos A ( 2 sin A - 1 ) - 1 ( 2 sin A - 1 ) = 0
=> ( 2 sin A - 1 ) ( cos A - 1 ) = 0

By Zero Product Rule,

2 sin A - 1 = 0 / ( cos A - 1 )
2 sin A - 1 = 0
2 sin A = 1
sin A = 1 / 2
sin A = sin 30 °
A = 30 °

OR

cos A - 1 = 0 / ( 2 sin A - 1 )
cos A - 1 = 0
cos A = 1
cos A = cos 0 °
A = 0 °

Hence,

A = 30° or 0°