Solve frac{sin(20^{circ})cos(20^{circ})}{{left(cos(25^circ)right)}^2-{left(sin(25^circ)right)}^2}

$$\frac{ \sin ( 20 ^ { \circ } ) \cos ( 20 ^ { \circ } ) }{ { \left( \cos ( 25 ^ { \circ } ) \right) }^{ 2 } - { \left( \sin ( 25 ^ { \circ } ) \right) }^{ 2 } }$$

Evaluate

$$\frac{267828170702724697969867472455900}{535656341405449340387752062294747}\approx 0.5$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.3420201433256687 \cdot 0.9396926207859084}{0.9063077870366499 ^ {2} - 0.42261826174069944 ^ {2}}$$

Multiply 0.3420201433256687 and 0.9396926207859084 to get 0.32139380484326963756384096694708.

$$\frac{0.32139380484326963756384096694708}{0.9063077870366499^{2}-0.42261826174069944^{2}}$$

Calculate 0.9063077870366499 to the power of 2 and get 0.82139380484326954852688581517001.

$$\frac{0.32139380484326963756384096694708}{0.82139380484326954852688581517001-0.42261826174069944^{2}}$$

Calculate 0.42261826174069944 to the power of 2 and get 0.1786061951567303400615833404163136.

$$\frac{0.32139380484326963756384096694708}{0.82139380484326954852688581517001-0.1786061951567303400615833404163136}$$

Subtract 0.1786061951567303400615833404163136 from 0.82139380484326954852688581517001 to get 0.6427876096865392084653024747536964.

$$\frac{0.32139380484326963756384096694708}{0.6427876096865392084653024747536964}$$

Expand \frac{0.32139380484326963756384096694708}{0.6427876096865392084653024747536964} by multiplying both numerator and the denominator by 10000000000000000000000000000000000.

$$\frac{3213938048432696375638409669470800}{6427876096865392084653024747536964}$$

Reduce the fraction \frac{3213938048432696375638409669470800}{6427876096865392084653024747536964} to lowest terms by extracting and canceling out 12.

$$\frac{267828170702724697969867472455900}{535656341405449340387752062294747}$$