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

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

Manatoko

Ngā Upane Otinga

Evaluate trigonometric functions in the problem

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

Tātaihia te 0.3420201433256687 mā te pū o 2, kia riro ko 0.11697777844051095979530830215969.

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

Tātaihia te 0.6427876096865394 mā te pū o 2, kia riro ko 0.41317591116653492029192554775236.

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

Tāpirihia te 0.11697777844051095979530830215969 ki te 0.41317591116653492029192554775236, ka 0.53015368960704588008723384991205.

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

Whakareatia te 0.3420201433256687 ki te 0.6427876096865394, ka 0.21984631039295419598585689389678.

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

Tāpirihia te 0.53015368960704588008723384991205 ki te 0.21984631039295419598585689389678, ka 0.75000000000000007607309074380883.

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

Me tahuri ki tau ā-ira 0.75000000000000007607309074380883 ki te hautau \frac{75000000000000007607309074380883}{10000000000}. Whakahekea te hautanga \frac{75000000000000007607309074380883}{10000000000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 1.

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

Ko te maha noa iti rawa atu o 100000000000000000000000000000000 me 4 ko 100000000000000000000000000000000. Me tahuri \frac{75000000000000007607309074380883}{100000000000000000000000000000000} me \frac{3}{4} ki te hautau me te tautūnga 100000000000000000000000000000000.

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

Whakatauritea te \frac{75000000000000007607309074380883}{100000000000000000000000000000000} me te \frac{75000000000000000000000000000000}{100000000000000000000000000000000}.

$$\text{false}$$