Solve 1/2-sin(75)sin(15)

$$\frac{ 1 }{ 2 } - \sin ( 75 ) \sin ( 15 )$$

Evaluate

$$0.250000000000000018157959763973458$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{1}{2} - 0.9659258262890683 \cdot 0.25881904510252074$$

Multiply 0.9659258262890683 and 0.25881904510252074 to get 0.249999999999999981842040236026542.

$$\frac{1}{2}-0.249999999999999981842040236026542$$

Convert decimal number 0.249999999999999981842040236026542 to fraction \frac{124999999999999990921020118013271}{10000000000}. Reduce the fraction \frac{124999999999999990921020118013271}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{1}{2}-\frac{124999999999999990921020118013271}{500000000000000000000000000000000}$$

Least common multiple of 2 and 500000000000000000000000000000000 is 500000000000000000000000000000000. Convert \frac{1}{2} and \frac{124999999999999990921020118013271}{500000000000000000000000000000000} to fractions with denominator 500000000000000000000000000000000.

$$\frac{250000000000000000000000000000000}{500000000000000000000000000000000}-\frac{124999999999999990921020118013271}{500000000000000000000000000000000}$$

Since \frac{250000000000000000000000000000000}{500000000000000000000000000000000} and \frac{124999999999999990921020118013271}{500000000000000000000000000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{250000000000000000000000000000000-124999999999999990921020118013271}{500000000000000000000000000000000}$$

Subtract 124999999999999990921020118013271 from 250000000000000000000000000000000 to get 125000000000000009078979881986729.

$$\frac{125000000000000009078979881986729}{500000000000000000000000000000000}$$