Question

sendo a - b = 60º, o valor de A = (cos a + cos b)² + (sen a + senb)² é

a) 3
b) 1
c) 1/2
d) -1/2
e) 3/2

Answer 1

a–b=60°

cos(a–b) =cos60°

cos(a–b)=½

cos(a-b)=cosacosb+senasenb

cosacosb+senasenb=½

(cosa+cosb)²+(sena+senb)²

=cos²a+2coscosb+cos²b+sen²a+2.sena.senb+sen²b

=cos²a+sen²a+cos²b+sen²b+2cosacob+2senasenb

=1+1+2cosacosb+2senasenb

=2+2cosacosb+2senasenb

=2(1+cosacosb+senasenb)

$= 2.(1 + \frac{1}{2} ) =2.( \frac{2 + 1}{2} ) \\ = 2. \frac{3}{2} = 3$letra a