Solve sin60^circ*cos30^circ+1/tan4

$$\sin 60 ^ { \circ } \cdot \cos 30 ^ { \circ } + \frac { 1 } { \tan 4 }$$

Evaluate

$$\frac{1055074157199173715830683993148479}{69926811943510410000000000000000}\approx 15.088263398$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.7875971414750719 + \frac{1}{0.06992681194351041}$$

Expand \frac{1}{0.06992681194351041} by multiplying both numerator and the denominator by 100000000000000000.

$$0.7875971414750719+\frac{100000000000000000}{6992681194351041}$$

Convert decimal number 0.7875971414750719 to fraction \frac{7875971414750719}{10000000000}. Reduce the fraction \frac{7875971414750719}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{7875971414750719}{10000000000000000}+\frac{100000000000000000}{6992681194351041}$$

Least common multiple of 10000000000000000 and 6992681194351041 is 69926811943510410000000000000000. Convert \frac{7875971414750719}{10000000000000000} and \frac{100000000000000000}{6992681194351041} to fractions with denominator 69926811943510410000000000000000.

$$\frac{55074157199173715830683993148479}{69926811943510410000000000000000}+\frac{1000000000000000000000000000000000}{69926811943510410000000000000000}$$

Since \frac{55074157199173715830683993148479}{69926811943510410000000000000000} and \frac{1000000000000000000000000000000000}{69926811943510410000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{55074157199173715830683993148479+1000000000000000000000000000000000}{69926811943510410000000000000000}$$

Add 55074157199173715830683993148479 and 1000000000000000000000000000000000 to get 1055074157199173715830683993148479.

$$\frac{1055074157199173715830683993148479}{69926811943510410000000000000000}$$