Question

Find the magnitude of angle A, if

2 sin A cos A - cos A -2 sin A + 1 = 0

• A. 90° , 60°
• B. 0° , 30°
• C. 30° , 60°
• D. 45° , 45°

Answer 1

The correct option is B

0° , 30°

Given that 2 sin A cos A - cos A -2 sin A + 1 = 0

Taking cos A common , we have

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

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

Hence ( cos A - 1) = 0 and ( 2 sin A -1 ) = 0

$\therefore$ cos A = 1 and 2 sin A = 1 ; sin A = $\frac{1}{2}$

A = 0° and A = 30 ° ( $\because$ Cos 0° = 1 and sin 30 ° = $\frac{1}{2}$)