Solve cos^8165^circ-sin^8165^circ

$$\cos ^ { 8 } 165 ^ { \circ } - \sin ^ { 8 } 165 ^ { \circ }$$

Evaluate

$$-0.75781249999999945568960102717487394974999718381959989728477112302504048497768661046378417659714301410509884745499703699869221376$$

Solution Steps

Evaluate trigonometric functions in the problem

$$-0.9659258262890682 ^ {8} - 0.258819045102521 ^ {8}$$

Calculate 0.9659258262890682 to the power of 8 and get 0.75779236415569136350081790672136971582782298524586095712879948771892348030627179931122480330449010245193559332263555763769221376.

$$-0.75779236415569136350081790672136971582782298524586095712879948771892348030627179931122480330449010245193559332263555763769221376-0.258819045102521^{8}$$

Calculate 0.258819045102521 to the power of 8 and get 0.000020135844308092188783120453504233922174198573738940155971635306117004671414811152559373292652911653163254132361479361.

$$-0.75779236415569136350081790672136971582782298524586095712879948771892348030627179931122480330449010245193559332263555763769221376-0.000020135844308092188783120453504233922174198573738940155971635306117004671414811152559373292652911653163254132361479361$$

Subtract 0.000020135844308092188783120453504233922174198573738940155971635306117004671414811152559373292652911653163254132361479361 from -0.75779236415569136350081790672136971582782298524586095712879948771892348030627179931122480330449010245193559332263555763769221376 to get -0.75781249999999945568960102717487394974999718381959989728477112302504048497768661046378417659714301410509884745499703699869221376.

$$-0.75781249999999945568960102717487394974999718381959989728477112302504048497768661046378417659714301410509884745499703699869221376$$