Ako tg a =2 , to cos a . cos 3 a e?

[diandimitrov]

Ako tg a =√2 , to cos a . cos 3 a e?
Shte sum vi blagodaren da mi pomognete s tazi zadacha

[dimy93]

[tex]cos2\alpha = \frac{1-tg^2\alpha }{ 1+tg^2\alpha } = \frac{1-2}{1+2 } = -\frac{1}{ 3}[/tex]
[tex]cos\alpha *cos3\alpha=\frac{cos2\alpha +cos4\alpha }{ 2}=\frac{2cos^22\alpha - 1 + cos2\alpha }{2 }[/tex]=
[tex]=\frac{2*\frac{1}{ 9}-\frac{1}{ 3} -1}{2 }= \frac{-\frac{10}{9 }}{2 }=-\frac{5}{ 9}[/tex]
толкова ли ти е отговора?

[diandimitrov]

da, mersi