Solve cos(75^circ)cos(105^circ)+sin(75^circ)sin(105^circ)

$$\cos ( 75 ^ { \circ } ) \cos ( 105 ^ { \circ } ) + \sin ( 75 ^ { \circ } ) \sin ( 105 ^ { \circ } )$$

Evaluate

$$0.866025403784438655459800018657461$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.25881904510252074 \cdot -0.25881904510252085 + 0.9659258262890683 \cdot 0.9659258262890683$$

Multiply 0.25881904510252074 and -0.25881904510252085 to get -0.066987298107780693519592063407429.

$$-0.066987298107780693519592063407429+0.9659258262890683\times 0.9659258262890683$$

Multiply 0.9659258262890683 and 0.9659258262890683 to get 0.93301270189221934897939208206489.

$$-0.066987298107780693519592063407429+0.93301270189221934897939208206489$$

Add -0.066987298107780693519592063407429 and 0.93301270189221934897939208206489 to get 0.866025403784438655459800018657461.

$$0.866025403784438655459800018657461$$