Question

Se Senx.Cosx= -1/2, ent]ao o valor de Cos(2x) é:
[ 25 pontos ]

Answer 1

$\displaystyle \sf \text{Sabendo que :} \\\\ 1) \ sen(2x) = 2\cdot sen(x)\cdot cos(x)\\\\ 2)\ sen^2(\theta)+cos^2(\theta) = 1 \\\\\\ \text{temos} : \\\\ sen(x)\cdot cos(x) = \frac{-1}{2} \ \ \cdot (2)\\\\ 2\cdot sen(x)\cdot cos(x) = \frac{-1\cdot 2}{2} \\\\\ sen(2x) = -1 \\\\ \text{Da{\'i} temos }: \\\\ sen^2(2x)+cos^2(2x)= 1 \\\\ (-1)^2+cos^2(2x) = 1 \\\\ 1+cos^2(2x) = 1 \\\\ cos^2(2x) = 0 \\\\ \huge\boxed{\sf cos(2x) = 0 \ }\checkmark$