Question

Trigonometrie

Transformati in produs


1 - 2cos a + cos 2a​

Answer 1

Răspuns:

$1-2*cos(a)+cos(2a)=1-2*cos(a)+cos^2a-sin^2a$

$=1-2*cos(a)+cos^2a-(1-cos^2a) =1-2*cos(a)+cos^2a-1+cos^2a$

$=-2*cos(a)+2*cos^2a = -2*cosa*(1-cosa)$

$=-2*cosa*(cos(0)-cos(a))$

$=-2cosa*(-2sin\frac{0+a}{2}*sin\frac{0-a}{2})$

$=-2*cosa*(-2sin\frac{a}{2}*(-sin\frac{a}{2}))$

$=-2*cosa*2sin^2\frac{a}{2}$

$=-4*cosa*sin^2\frac{a}{2}$