Solve sin^265^circ+sin^225^circ

$$\sin ^ { 2 } 65 ^ { \circ } + \sin ^ { 2 } 25 ^ { \circ }$$

Evaluate

$$0.9999999999999998885884691555863236$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.9063077870366499 ^ {2} + 0.42261826174069944 ^ {2}$$

Calculate 0.9063077870366499 to the power of 2 and get 0.82139380484326954852688581517001.

$$0.82139380484326954852688581517001+0.42261826174069944^{2}$$

Calculate 0.42261826174069944 to the power of 2 and get 0.1786061951567303400615833404163136.

$$0.82139380484326954852688581517001+0.1786061951567303400615833404163136$$

Add 0.82139380484326954852688581517001 and 0.1786061951567303400615833404163136 to get 0.9999999999999998885884691555863236.

$$0.9999999999999998885884691555863236$$

Factor

$$\frac{521 \cdot 533162721262529264549194474081 \cdot 3 ^ {2}}{2 ^ {32} \cdot 5 ^ {34}} = 1\frac{2.8823037615171176 \times 10^{17}}{2.5 \times 10^{33}} = 1.0000000000000002$$