Solve sin^{2}20+sin^240^circ+sin^280^circ=3/2

$$\sin ^ { 2 } 20 + \sin ^ { 2 } 40 ^ { \circ } + \sin ^ { 2 } 80 ^ { \circ } = \frac { 3 } { 2 }$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$0.3420201433256687 ^ {2} + 0.6427876096865393 ^ {2} + 0.984807753012208 ^ {2} = \frac{3}{2}$$

Calculate 0.3420201433256687 to the power of 2 and get 0.11697777844051095979530830215969.

$$0.11697777844051095979530830215969+0.6427876096865393^{2}+0.984807753012208^{2}=\frac{3}{2}$$

Calculate 0.6427876096865393 to the power of 2 and get 0.41317591116653479173440361044449.

$$0.11697777844051095979530830215969+0.41317591116653479173440361044449+0.984807753012208^{2}=\frac{3}{2}$$

Add 0.11697777844051095979530830215969 and 0.41317591116653479173440361044449 to get 0.53015368960704575152971191260418.

$$0.53015368960704575152971191260418+0.984807753012208^{2}=\frac{3}{2}$$

Calculate 0.984807753012208 to the power of 2 and get 0.969846310392954075097397035264.

$$0.53015368960704575152971191260418+0.969846310392954075097397035264=\frac{3}{2}$$

Add 0.53015368960704575152971191260418 and 0.969846310392954075097397035264 to get 1.49999999999999982662710894786818.

$$1.49999999999999982662710894786818=\frac{3}{2}$$

Convert decimal number 1.49999999999999982662710894786818 to fraction \frac{74999999999999991331355447393409}{10000000000}. Reduce the fraction \frac{74999999999999991331355447393409}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{74999999999999991331355447393409}{50000000000000000000000000000000}=\frac{3}{2}$$

Least common multiple of 50000000000000000000000000000000 and 2 is 50000000000000000000000000000000. Convert \frac{74999999999999991331355447393409}{50000000000000000000000000000000} and \frac{3}{2} to fractions with denominator 50000000000000000000000000000000.

$$\frac{74999999999999991331355447393409}{50000000000000000000000000000000}=\frac{75000000000000000000000000000000}{50000000000000000000000000000000}$$

Compare \frac{74999999999999991331355447393409}{50000000000000000000000000000000} and \frac{75000000000000000000000000000000}{50000000000000000000000000000000}.

$$\text{false}$$