Question

Me ajuda a calcular cos(5pi/24)*cos(pi/24)

Answer 1

Dedução da fórmula
cos(a+b) = cosa.cosb - sena.senb
cos(a-b) =  cosa.cosb + sena.senb
___________________________..

cos(a+b)+cos(a-b) = 2cosa.cosb

cos5π/24.cosπ/24

cos(5π/24+π/24)+cos(5π/24 -π/24) = 2cos(5π/24).cos(π/24)

cos(π/4)+cos(π/6) = 2cos(5pi/24)cos(pi/24) 

[√2/2 + 1/2] =  2cos(5pi/24)cos(pi/24)  

[√2/2 + 1/2]/2 = cos(5pi/24)*cos(pi/24)

[(√2+1)/2]/2 =  cos(5pi/24)cos(pi/24) 

[(√2+1)/4 =  cos(5pi/24)cos(pi/24)