Khẳng định nào trong các khẳng định dưới đây là đúng?
(I) \(4x^2\cos^260^0-2xy\cos^3180^0+\dfrac{4}{3}y^2\cos^230^0=\left(x-y\right)^2\)
(II) \(\left(a\sin90^0+b\tan45^0\right)\left(a\cos0^0+b\cos180^0\right)=a^2-b^2\)
(III) \(4x^2\cos^260^0+2xy\cos^2180^0+\dfrac{4}{3}y^2\cos^230^0=\left(x+y\right)^2\)
(IV) \(\left(a\sin90^0+b\tan135^0\right)\left(a\cos0^0+b\cos0^0\right)=a^2-b^2\)
II) và (III).(I), (II) và (III).(II), (III) và (IV).(III) và (IV).Hướng dẫn giải:a) \(4x^2\cos^260^0+2xy\cos^2180^0+\dfrac{4}{3}y^2\cos^230^0=4x^2\left(\dfrac{1}{2}\right)^2+2xy\left(-1\right)^2+\dfrac{4}{3}y^2\left(\dfrac{\sqrt{3}}{2}\right)^2=x^2+2xy+y^2=\left(x+y\right)^2\)
b) \(4x^2\cos^260^0-2xy\cos^3180^0+\dfrac{4}{3}y^2\cos^230^0=4x^2\left(\dfrac{1}{2}\right)^2-2xy\left(-1\right)^3+\dfrac{4}{3}y^2\left(\dfrac{\sqrt{3}}{2}\right)^2=x^2+2xy+y^2=\left(x+y\right)^2\)
c) \(\left(a\sin90^0+b\tan45^0\right)\left(a\cos0^0+b\cos180^0\right)=\left(a.1+b.1\right)\left(a.1+b.\left(-1\right)\right)=a^2-b^2\)
d) \(\left(a\sin90^0+b\tan135^0\right)\left(a\cos0^0+b\cos0^0\right)=\left(a.1+b.\left(-1\right)\right)\left(a.1+b.1\right)=a^2-b^2\)
