Question

Como simplificar a expressão A= sen 2x/sen x = cos 2x/cos x

Answer 1

Resposta:

Sen (2×)=2 sen (x) cos (x) (I)

cos (2×)=Cos2 (x) (II)

substituindo (I) e (II)

obs: o dois no cos fico grande pq eu nao consegui coloca pequeno

Answer 2

Resposta:

Explicação passo-a-passo:

$A=\dfrac{sen(2x)}{sen(x)}-\dfrac{cos(2x)}{cos(x)}\\\\mmc(sen(x),cos(x))=sen(x).cos(x)\\\\A=\dfrac{cos(x).sen(2x)-sen(x).cos(2x)}{sen(x).cos(x)}\\\\\\sen(2x)=2sen(x).cos(x)\\\\e\\\\cos(2x)=cos^{2}(x)-sen^{2}(x)\\\\\\\\A=\dfrac{cos(x).2sen(x).cos(x)-sen(x).(cos^{2}(x)-sen^{2}(x))}{sen(x).cos(x)}\\\\\\A=\dfrac{2.cos^{2} (x).sen(x)-sen(x).(cos^{2}(x)-sen^{2}(x))}{sen(x).cos(x)}\\\\\\A=\dfrac{sen(x).[2.cos^{2} (x)-(cos^{2}(x)-sen^{2}(x))]}{sen(x).cos(x)}$

$A=\dfrac{2.cos^{2} (x)-cos^{2}(x)+sen^{2}(x)}{cos(x)}\\\\\\A=\dfrac{cos^{2} (x)+sen^{2}(x)}{cos(x)}\\\\\\A=\dfrac{1}{cos(x)}\\\\\\A=sec(x)$