Question

Va rog urgent!!!!!!!!! ​

Answer 1

Explicație pas cu pas:

a)

$\sin(60) = \cos(90 - 60) = \cos(30) \\ tg(45) = ctg(45)$

=>

$\sin(60) + \tg(45) = \cos(30) + \ctg(45)$

$\sin(60) = \frac{ \sqrt{3} }{2} ; tg(45) = 1 ; \cos(30) = \frac{ \sqrt{3} }{2} ; ctg(45) = 1$

b)

$\sin(120) = \cos(90 - 120) = \cos( - 30) = - \cos(30) \\ = > \sin^{2} (120) = \cos^{2} (30)$

=>

$\sin^{2} (120) - \cos^{2} (30) = 0$

$\cos(30) = \frac{ \sqrt{3} }{2}$

c)

$\sin (135) = \cos(90 - 135) = \cos( - 45) = - \cos( - 45)\\ = > \sin^{2} (135) = \cos^{2} (45)$

=>

$\cos^{2} (45) + \sin^{2} (45) = 1$

$\sin(45) = \frac{ \sqrt{2} }{2} ; \cos(45) = \frac{ \sqrt{2} }{2}$

d)

$\sin^{2} (45) - \cos^{2} (60) = {\left( \frac{ \sqrt{2} }{2} \right)}^{2} - {\left( \frac{1}{2} \right)}^{2} \\ = \frac{2}{4} - \frac{1}{4} = \frac{1}{4}$