Solve cossin25^circ/cos65^circ+tan23^circ/cot67^circ

$$\cos \frac { \sin 25 ^ { \circ } } { \cos 65 ^ { \circ } } + \frac { \tan 23 ^ { \circ } } { \cot 67 ^ { \circ } }$$

Evaluate

$$\frac{84888498284871096444998668279737}{42447481620960490000000000000000}\approx 1.999847695$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.9998476951563913 + \frac{0.4244748162096047}{0.4244748162096049}$$

Expand \frac{0.4244748162096047}{0.4244748162096049} by multiplying both numerator and the denominator by 10000000000000000.

$$0.9998476951563913+\frac{4244748162096047}{4244748162096049}$$

Convert decimal number 0.9998476951563913 to fraction \frac{9998476951563913}{10000000000}. Reduce the fraction \frac{9998476951563913}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{9998476951563913}{10000000000000000}+\frac{4244748162096047}{4244748162096049}$$

Least common multiple of 10000000000000000 and 4244748162096049 is 42447481620960490000000000000000. Convert \frac{9998476951563913}{10000000000000000} and \frac{4244748162096047}{4244748162096049} to fractions with denominator 42447481620960490000000000000000.

$$\frac{42441016663910626444998668279737}{42447481620960490000000000000000}+\frac{42447481620960470000000000000000}{42447481620960490000000000000000}$$

Since \frac{42441016663910626444998668279737}{42447481620960490000000000000000} and \frac{42447481620960470000000000000000}{42447481620960490000000000000000} have the same denominator, add them by adding their numerators.

$$\frac{42441016663910626444998668279737+42447481620960470000000000000000}{42447481620960490000000000000000}$$

Add 42441016663910626444998668279737 and 42447481620960470000000000000000 to get 84888498284871096444998668279737.

$$\frac{84888498284871096444998668279737}{42447481620960490000000000000000}$$