Solve left(cos(18)right)^2-left(sin(18)right)^2

$${ \left( \cos ( 18 ) \right) }^{ 2 } - { \left( \sin ( 18 ) \right) }^{ 2 }$$

Evaluate

$$0.80901699437494730182471083579549$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.9510565162951535 ^ {2} - 0.3090169943749474 ^ {2}$$

Calculate 0.9510565162951535 to the power of 2 and get 0.90450849718747357487752758856225.

$$0.90450849718747357487752758856225-0.3090169943749474^{2}$$

Calculate 0.3090169943749474 to the power of 2 and get 0.09549150281252627305281675276676.

$$0.90450849718747357487752758856225-0.09549150281252627305281675276676$$

Subtract 0.09549150281252627305281675276676 from 0.90450849718747357487752758856225 to get 0.80901699437494730182471083579549.

$$0.80901699437494730182471083579549$$

Factor

$$\frac{3 \cdot 19 \cdot 29 \cdot 1429 \cdot 58099 \cdot 89491 \cdot 77332291 \cdot 85181183}{2 ^ {32} \cdot 5 ^ {32}} = 0.8090169943749472$$