Question

Cum as putea rezolva un astfel tip de exercitiu? sin a +cos a/sin a- cos a = ? (este vorba de formulele de transformare a sumei in produs,iar aici ar trebui sa simplific)

Answer 1

$\frac{sina+cosa}{sina-cosa} = \frac{ (sina+cosa)^{2} }{sin^{2}a-cos^{2}a} = \frac{sin^{2}a+cos^{2}a+2sinacosa}{-(cos^{2}a-sin^{2}a)}$
Utilizand formulele trigonometrice vei obtine:
$\frac{1+sin2a}{-cos2a }=\frac{1+sin2a}{- \sqrt{1-sin^{2}2a} } = \frac{1+sin2a}{-( \sqrt{1+sin2a} )( \sqrt{1-sin2a} )} =- \frac{ \sqrt{1+sin2a} }{ \sqrt{1-sin2a} }$
$=- \sqrt{ \frac{2-1+sin2a}{1-sin2a} } = \sqrt{ \frac{2}{1-sin2a}-1 }$