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

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

Tarkista

Ratkaisun vaiheet

Evaluate trigonometric functions in the problem

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

Laske 0,3420201433256687 potenssiin 2, jolloin ratkaisuksi tulee 0,11697777844051095979530830215969.

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

Laske 0,6427876096865394 potenssiin 2, jolloin ratkaisuksi tulee 0,41317591116653492029192554775236.

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

Selvitä 0,53015368960704588008723384991205 laskemalla yhteen 0,11697777844051095979530830215969 ja 0,41317591116653492029192554775236.

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

Kerro 0,3420201433256687 ja 0,6427876096865394, niin saadaan 0,21984631039295419598585689389678.

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

Selvitä 0,75000000000000007607309074380883 laskemalla yhteen 0,53015368960704588008723384991205 ja 0,21984631039295419598585689389678.

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

Muunna desimaaliluku 0,75000000000000007607309074380883 murtoluvuksi \frac{75000000000000007607309074380883}{10000000000}. Supista murtoluku \frac{75000000000000007607309074380883}{10000000000} luvulla 1.

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

Lukujen 100000000000000000000000000000000 ja 4 pienin yhteinen jaettava on 100000000000000000000000000000000. Muunna \frac{75000000000000007607309074380883}{100000000000000000000000000000000} ja \frac{3}{4} murtoluvuiksi, joiden nimittäjä on 100000000000000000000000000000000.

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

Vertaa kohteita \frac{75000000000000007607309074380883}{100000000000000000000000000000000} ja \frac{75000000000000000000000000000000}{100000000000000000000000000000000}.

$$\text{false}$$