Solve 1-left(cos(110)right)^2-left(cos(80)right)^2

$$1- { \left( \cos ( 110 ) \right) }^{ 2 } - { \left( \cos ( 80 ) \right) }^{ 2 }$$

Evaluate

$$1.0868240888334651305857869903769219$$

Solution Steps

Evaluate trigonometric functions in the problem

$$1 - -0.3420201433256687 ^ {2} - 0.17364817766693041 ^ {2}$$

Calculate 0.3420201433256687 to the power of 2 and get 0.11697777844051095979530830215969.

$$1-\left(-0.11697777844051095979530830215969\right)-0.17364817766693041^{2}$$

The opposite of -0.11697777844051095979530830215969 is 0.11697777844051095979530830215969.

$$1+0.11697777844051095979530830215969-0.17364817766693041^{2}$$

Add 1 and 0.11697777844051095979530830215969 to get 1.11697777844051095979530830215969.

$$1.11697777844051095979530830215969-0.17364817766693041^{2}$$

Calculate 0.17364817766693041 to the power of 2 and get 0.0301536896070458292095213117827681.

$$1.11697777844051095979530830215969-0.0301536896070458292095213117827681$$

Subtract 0.0301536896070458292095213117827681 from 1.11697777844051095979530830215969 to get 1.0868240888334651305857869903769219.

$$1.0868240888334651305857869903769219$$

Factor

$$\frac{11 \cdot 13 \cdot 76001684533808750390614474851533}{2 ^ {34} \cdot 5 ^ {34}} = 1\frac{8.682408883346518 \times 10^{32}}{1 \times 10^{34}} = 1.0868240888334653$$