Question

2. Se cos X - sen x 12 então sen (2x) é igual a a) 0,125. b) 0,25. c) 0,5. d) 0,75. e) 1.​

Answer 1

$\large\boxed{\begin{array}{l}\rm cos(x)-sen(x)=\dfrac{1}{2}\\\rm (cos(x)-sen(x))^2=\bigg(\dfrac{1}{2}\bigg)^2\\\\\rm cos^2(x)-2\cdot cos(x)\cdot sen(x)+sen^2(x)=\dfrac{1}{4}\\\rm cos^2(x)+sen^2(x)-sen(2x)=\dfrac{1}{4}\\\\\rm 1-sen(2x)=\dfrac{1}{4}\\\\\rm sen(2x)=1-\dfrac{1}{4}\\\\\rm sen(2x)=\dfrac{4-1}{4}\\\\\rm sen(2x)=\dfrac{3}{4}\\\\\rm sen(2x)=0,75\\\huge\boxed{\boxed{\boxed{\boxed{\rm\dagger\red{\maltese}~\blue{alternativa~d}}}}}\end{array}}$