Question

2sin^2 (45 -a) = sin2a

Answer 1

Ответ:

$2 { \sin}^{2} (45 - \alpha ) = 2 {( \sin(45 - \alpha )) }^{2} = \\ = 2 {( \sin(45) \cos( \alpha ) - \sin( \alpha ) \cos(45) )}^{2} = \\ = 2 {( \frac{ \sqrt{2} }{2} \cos( \alpha ) - \frac{ \sqrt{2} }{2} \sin( \alpha ) )}^{2} = \\ = 2 {( \frac{ \sqrt{2} }{2}( \cos( \alpha ) - \sin( \alpha )) }^{2} = \\ = 2 \times \frac{1}{2} {( \cos( \alpha ) - \sin( \alpha )) }^{2} = \\ = { \cos }^{2} \alpha - 2 \sin( \alpha ) \cos( \alpha ) + { \sin}^{2} \alpha = \\ = 1 - \sin(2 \alpha )$