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

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

Verify

Solution Steps

Evaluate trigonometric functions in the problem

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

Calculate 0.3420201433256687 to the power of 2 and get 0.11697777844051095979530830215969.

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

Calculate 0.6427876096865394 to the power of 2 and get 0.41317591116653492029192554775236.

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

Add 0.11697777844051095979530830215969 and 0.41317591116653492029192554775236 to get 0.53015368960704588008723384991205.

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

Multiply 0.3420201433256687 and 0.6427876096865394 to get 0.21984631039295419598585689389678.

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

Add 0.53015368960704588008723384991205 and 0.21984631039295419598585689389678 to get 0.75000000000000007607309074380883.

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

Convert decimal number 0.75000000000000007607309074380883 to fraction \frac{75000000000000007607309074380883}{10000000000}. Reduce the fraction \frac{75000000000000007607309074380883}{10000000000} to lowest terms by extracting and canceling out 1.

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

Least common multiple of 100000000000000000000000000000000 and 4 is 100000000000000000000000000000000. Convert \frac{75000000000000007607309074380883}{100000000000000000000000000000000} and \frac{3}{4} to fractions with denominator 100000000000000000000000000000000.

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

Compare \frac{75000000000000007607309074380883}{100000000000000000000000000000000} and \frac{75000000000000000000000000000000}{100000000000000000000000000000000}.

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