TÍNH P = sin^4 a + cos^4 a biết : sin a.cos a = 1/2 31/10/2021 Bởi Alaia TÍNH P = sin^4 a + cos^4 a biết : sin a.cos a = 1/2
$P= sin^4a+cos^4a= (sin^2a)^2+(cos^2a)^2= (sin^2a+cos^2a)^2-2sin^2a.cos^2a=1-2.\frac{1}{4}=\frac{1}{2}$ Bình luận
P = $sin^{4}$$\alpha$ + $cos^{4}$$\alpha$ = $sin^{4}$$\alpha$ + $cos^{4}$$\alpha$ + 2.$sin^{2}$$\alpha$.$cos^{2}$$\alpha$ – 2.$sin^{2}$$\alpha$.$cos^{2}$$\alpha$ = ($sin^{2}$$\alpha$ + $cos^{2}$$\alpha$)$^{2}$ – 2.$sin^{2}$$\alpha$.$cos^{2}$$\alpha$ = $1^{2}$ – 2.$\frac{1}{2}$ .$\frac{1}{2}$ = $\frac{1}{2}$ Vậy P = $\frac{1}{2}$ Bình luận
$P= sin^4a+cos^4a= (sin^2a)^2+(cos^2a)^2= (sin^2a+cos^2a)^2-2sin^2a.cos^2a=1-2.\frac{1}{4}=\frac{1}{2}$
P = $sin^{4}$$\alpha$ + $cos^{4}$$\alpha$ = $sin^{4}$$\alpha$ + $cos^{4}$$\alpha$ + 2.$sin^{2}$$\alpha$.$cos^{2}$$\alpha$ – 2.$sin^{2}$$\alpha$.$cos^{2}$$\alpha$ = ($sin^{2}$$\alpha$ + $cos^{2}$$\alpha$)$^{2}$ – 2.$sin^{2}$$\alpha$.$cos^{2}$$\alpha$ = $1^{2}$ – 2.$\frac{1}{2}$ .$\frac{1}{2}$ = $\frac{1}{2}$
Vậy P = $\frac{1}{2}$