Question

sin a+cos a=2/5. sa se calculeze sin 2a

Answer 1

Răspuns:

Explicație pas cu pas:

$\sin a+\cos a=\dfrac{2}{5}|()^2\\(\sin a+\cos a)^2=\dfrac{4}{25}\\\sin^2 a+2\cdot\sin a\cdot\cos a+\cos^2 a=\dfrac{4}{25}\\1+\sin2a=\dfrac{4}{25}\\\sin2a=\dfrac{4}{25}-1\\\boxed{\sin2a=-\dfrac{21}{25}}\\\texttt{Am aplicat formulele:}\\\bullet \sin^2a+\cos^2 a=1\\\bullet 2\sin a\cdot\cos a=\sin 2a\\\bullet (a+b)^2=a^2+2ab+b^2$