Løs sin^{2}20^{circ}+cos^250^circ+sin20^circcos50^circ=3/4

$$\sin ^ { 2 } 20 ^ { \circ } + \cos ^ { 2 } 50 ^ { \circ } + \sin 20 ^ { \circ } \cos 50 ^ { \circ } = \frac { 3 } { 4 }$$

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Løsningstrinn

Evaluate trigonometric functions in the problem

$$0,3420201433256687 ^ {2} + 0,6427876096865394 ^ {2} + 0,3420201433256687 \cdot 0,6427876096865394 = \frac{3}{4}$$

Regn ut 0,3420201433256687 opphøyd i 2 og få 0,11697777844051095979530830215969.

$$0,11697777844051095979530830215969+0,6427876096865394^{2}+0,3420201433256687\times 0,6427876096865394=\frac{3}{4}$$

Regn ut 0,6427876096865394 opphøyd i 2 og få 0,41317591116653492029192554775236.

$$0,11697777844051095979530830215969+0,41317591116653492029192554775236+0,3420201433256687\times 0,6427876096865394=\frac{3}{4}$$

Legg sammen 0,11697777844051095979530830215969 og 0,41317591116653492029192554775236 for å få 0,53015368960704588008723384991205.

$$0,53015368960704588008723384991205+0,3420201433256687\times 0,6427876096865394=\frac{3}{4}$$

Multipliser 0,3420201433256687 med 0,6427876096865394 for å få 0,21984631039295419598585689389678.

$$0,53015368960704588008723384991205+0,21984631039295419598585689389678=\frac{3}{4}$$

Legg sammen 0,53015368960704588008723384991205 og 0,21984631039295419598585689389678 for å få 0,75000000000000007607309074380883.

$$0,75000000000000007607309074380883=\frac{3}{4}$$

Konverter desimaltallet 0,75000000000000007607309074380883 til brøken \frac{75000000000000007607309074380883}{10000000000}. Forkort brøken \frac{75000000000000007607309074380883}{10000000000} til minste felles nevner ved å dele teller og nevner på 1.

$$\frac{75000000000000007607309074380883}{100000000000000000000000000000000}=\frac{3}{4}$$

Minste felles multiplum av 100000000000000000000000000000000 og 4 er 100000000000000000000000000000000. Konverter \frac{75000000000000007607309074380883}{100000000000000000000000000000000} og \frac{3}{4} til brøker med nevner 100000000000000000000000000000000.

$$\frac{75000000000000007607309074380883}{100000000000000000000000000000000}=\frac{75000000000000000000000000000000}{100000000000000000000000000000000}$$

Sammenlign \frac{75000000000000007607309074380883}{100000000000000000000000000000000} og \frac{75000000000000000000000000000000}{100000000000000000000000000000000}.

$$\text{false}$$