Tính $S=sin^2 20^0+sin^2 50^0+sin^2 70^0+sin^2 100^0-\frac{\sqrt{3}}{2}cos50^0$

Question

Tính

$S=sin^2 20^0+sin^2 50^0+sin^2 70^0+sin^2 100^0-\frac{\sqrt{3}}{2}cos50^0$

score 0 · Answer 1

$S$

$=$

$\sin^{2}$

$20^{0}$

$+ \sin^{2}$

$70^{0}$

$+ \sin^{2}$

$50^{0}$

$+ \sin^{2}$

$100^{0}$

$-\frac{\sqrt{3}}{2}$

$\cos 50^{0}$

$\sin^{2}$

$20^{0}$

$+ \sin^{2}$

$70^{0}$

$=$

$1$

$( 2 góc phụ nhau )$

$\Rightarrow$

$S$

$=$

$1$

$+ \sin^{2}$

$50^{0}$

$+ \sin^{2}$

$100^{0}$

$-\frac{\sqrt{3}}{2}$

$\cos 50^{0}$

$\left ( 1\right )$

$=$

$1$

$+ \frac{1-\cos 100^{0} +1 - \cos 200^{0}}{2}$

$-\frac{\sqrt{3}}{2}$

$\cos 50^{0}$

$=$

$1$

$+ 1$

$- \frac{1}{2}$

$\left ( \cos 100^{0} + \cos 200^{0} \right )$

$- \cos 30^{0}$

$\cos 50^{0}$

$=$

$1$

$+ 1$

$- \cos 150^{0}$

$\cos 50^{0}$

$- \cos 30^{0}$

$\cos 50^{0}$

$=$

$1$

$+ 1$

$- \cos 50^{0}$

$\left ( \cos 150^{0}+ \cos 30^{0} \right )$

$=$

$1$

$+ 1$

$- \cos 50^{0}$

$\left ( - \cos 30^{0}+ \cos 30^{0} \right )$

$=$

$1$

$+ 1$

$+ 0$

$=$

$2$

Hỏi	25-04-13 08:46 PM
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Hoạt động	26-04-13 03:13 AM

Tính $S=sin^2 20^0+sin^2 50^0+sin^2 70^0+sin^2 100^0-\frac{\sqrt{3}}{2}cos50^0$

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Tính S=sin2200+sin2500+sin2700+sin21000−√32cos500S=sin^2 20^0+sin^2 50^0+sin^2 70^0+sin^2 100^0-\frac{\sqrt{3}}{2}cos50^0

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Liên quan

Tính $S=sin^2 20^0+sin^2 50^0+sin^2 70^0+sin^2 100^0-\frac{\sqrt{3}}{2}cos50^0$