Question

Daca sin(u)+cos(u)=$\frac{5}{4}$, atunci calculati sin2u si cos4u

Answer 1

( sinu + cosu )^2 = 25 / 16 <=> 1 + sin(2u) = 25 / 16 <=> sin(2u) = 9 / 16 ;
Am aplicat 3 formule :
a) ( x + y )^2 = x^2 + y^2 + 2xy ;
b) ( sinu )^2 + ( cosu )^2 = 1 ;
c) 2sinucosu = sin(2u);

cos(4u) = 1 - 2[sin(2u)]^2 = 1 - 2 × ( 81 / 256 ) = 1 - 81 / 128 = 47 / 128 ;
Am aplicat formula cos(2y) = 1 - 2(siny)^2 ;

Bafta !

Answer 2

Aplici formula :    cos(2y) = 1 - 2(siny)^2