Solve cos^210^circ+cos^250^circ-sin40sin80

$$\cos ^ { 2 } 10 ^ { \circ } + \cos ^ { 2 } 50 ^ { \circ } - \sin 40 \sin 80$$

Evaluate

$$0.75000000000000004187107641124196$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.984807753012208 ^ {2} + 0.6427876096865394 ^ {2} - 0.6427876096865393 \cdot 0.984807753012208$$

Calculate 0.984807753012208 to the power of 2 and get 0.969846310392954075097397035264.

$$0.969846310392954075097397035264+0.6427876096865394^{2}-0.6427876096865393\times 0.984807753012208$$

Calculate 0.6427876096865394 to the power of 2 and get 0.41317591116653492029192554775236.

$$0.969846310392954075097397035264+0.41317591116653492029192554775236-0.6427876096865393\times 0.984807753012208$$

Add 0.969846310392954075097397035264 and 0.41317591116653492029192554775236 to get 1.38302222155948899538932258301636.

$$1.38302222155948899538932258301636-0.6427876096865393\times 0.984807753012208$$

Multiply 0.6427876096865393 and 0.984807753012208 to get 0.6330222215594889535182461717744.

$$1.38302222155948899538932258301636-0.6330222215594889535182461717744$$

Subtract 0.6330222215594889535182461717744 from 1.38302222155948899538932258301636 to get 0.75000000000000004187107641124196.

$$0.75000000000000004187107641124196$$

Factor

$$\frac{4357 \cdot 35869 \cdot 84349 \cdot 88037 \cdot 461599 \cdot 35001319}{2 ^ {30} \cdot 5 ^ {32}} = 0.75$$