Solve cos(20)=1-2(5/sqrt{81})

$$\cos ( 20 ) = 1 - 2 ( 5 / \sqrt { 81 } )$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$0.9396926207859084 = 1 - 2 {(5 / \sqrt{81})}$$

Calculate the square root of 81 and get 9.

$$0.9396926207859084=1-2\times \frac{5}{9}$$

Express 2\times \frac{5}{9} as a single fraction.

$$0.9396926207859084=1-\frac{2\times 5}{9}$$

Multiply 2 and 5 to get 10.

$$0.9396926207859084=1-\frac{10}{9}$$

Convert 1 to fraction \frac{9}{9}.

$$0.9396926207859084=\frac{9}{9}-\frac{10}{9}$$

Since \frac{9}{9} and \frac{10}{9} have the same denominator, subtract them by subtracting their numerators.

$$0.9396926207859084=\frac{9-10}{9}$$

Subtract 10 from 9 to get -1.

$$0.9396926207859084=-\frac{1}{9}$$

Convert decimal number 0.9396926207859084 to fraction \frac{2349231551964771}{10000000000}. Reduce the fraction \frac{2349231551964771}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{2349231551964771}{2500000000000000}=-\frac{1}{9}$$

Least common multiple of 2500000000000000 and 9 is 22500000000000000. Convert \frac{2349231551964771}{2500000000000000} and -\frac{1}{9} to fractions with denominator 22500000000000000.

$$\frac{21143083967682939}{22500000000000000}=-\frac{2500000000000000}{22500000000000000}$$

Compare \frac{21143083967682939}{22500000000000000} and -\frac{2500000000000000}{22500000000000000}.

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