Question

dem ca sin^4x-sin²x=cos^4x-cos²x , pt orice x apartine lui R
cum se rezolva?

Answer 1

Explicație pas cu pas:

Folosim formula fundamentala a trigonometriei:

$\sin^2x+\cos^2x=1\\\sin^2x=1-\cos^2x$

Ridicam la patrat si avem:

$\sin^2x=1-\cos^2x|^2\\(\sin^2x)^2=(1-\cos^2x)^2\\\sin^4x=1+\cos^4x-2\cos^2x$

Si atunci membrul stang devine:

$\sin^4x-\sin^2x=1+\cos^4x-2\cos^2x-(1-\cos^2x)=1+\cos^4x-2\cos^2x-1+\cos^2x=\cos^4x-\cos^2x$