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

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

Staðfesta

Lausnarskref

Evaluate trigonometric functions in the problem

$$0.3420201433256687 ^ {2} + 0.6427876096865394 ^ {2} + 0.3420201433256687 \cdot 0.6427876096865394 = \frac{3}{4}$$

Reiknaðu 0.3420201433256687 í 2. veldi og fáðu 0.11697777844051095979530830215969.

$$0.11697777844051095979530830215969+0.6427876096865394^{2}+0.3420201433256687\times 0.6427876096865394=\frac{3}{4}$$

Reiknaðu 0.6427876096865394 í 2. veldi og fáðu 0.41317591116653492029192554775236.

$$0.11697777844051095979530830215969+0.41317591116653492029192554775236+0.3420201433256687\times 0.6427876096865394=\frac{3}{4}$$

Leggðu saman 0.11697777844051095979530830215969 og 0.41317591116653492029192554775236 til að fá 0.53015368960704588008723384991205.

$$0.53015368960704588008723384991205+0.3420201433256687\times 0.6427876096865394=\frac{3}{4}$$

Margfaldaðu 0.3420201433256687 og 0.6427876096865394 til að fá út 0.21984631039295419598585689389678.

$$0.53015368960704588008723384991205+0.21984631039295419598585689389678=\frac{3}{4}$$

Leggðu saman 0.53015368960704588008723384991205 og 0.21984631039295419598585689389678 til að fá 0.75000000000000007607309074380883.

$$0.75000000000000007607309074380883=\frac{3}{4}$$

Breyta tugabrotinu 0.75000000000000007607309074380883 í brot \frac{75000000000000007607309074380883}{10000000000}. Minnka brotið \frac{75000000000000007607309074380883}{10000000000} eins mikið og hægt er með því að draga og stytta út 1.

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

Sjaldgæfasta margfeldi 100000000000000000000000000000000 og 4 er 100000000000000000000000000000000. Breyttu \frac{75000000000000007607309074380883}{100000000000000000000000000000000} og \frac{3}{4} í brot með nefnaranum 100000000000000000000000000000000.

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

Bera saman \frac{75000000000000007607309074380883}{100000000000000000000000000000000} og \frac{75000000000000000000000000000000}{100000000000000000000000000000000}.

$$\text{false}$$