Solve =frac{sin25^{circ}+tan36^{circ}+sec24^circ}{cos65^circ+cot55^circ+cos66^circ}

$$= \frac { \sin 25 ^ { \circ } + \tan 36 ^ { \circ } + \sec 24 ^ { \circ } } { \cos 65 ^ { \circ } + \cot 55 ^ { \circ } + \cos 66 ^ { \circ } }$$

Evaluate

$$\frac{14023731676575669}{9559765268913809}\approx 1.466953558$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.42261826174069944 + 0.7265425280053608 + 1.0946362785060468}{0.42261826174069944 + 0.7002075382097098 + 0.4067366430758002}$$

Add 0.42261826174069944 and 0.7265425280053608 to get 1.14916078974606024.

$$\frac{1.14916078974606024+1.0946362785060468}{0.42261826174069944+0.7002075382097098+0.4067366430758002}$$

Add 1.14916078974606024 and 1.0946362785060468 to get 2.24379706825210704.

$$\frac{2.24379706825210704}{0.42261826174069944+0.7002075382097098+0.4067366430758002}$$

Add 0.42261826174069944 and 0.7002075382097098 to get 1.12282579995040924.

$$\frac{2.24379706825210704}{1.12282579995040924+0.4067366430758002}$$

Add 1.12282579995040924 and 0.4067366430758002 to get 1.52956244302620944.

$$\frac{2.24379706825210704}{1.52956244302620944}$$

Expand \frac{2.24379706825210704}{1.52956244302620944} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{224379706825210704}{152956244302620944}$$

Reduce the fraction \frac{224379706825210704}{152956244302620944} to lowest terms by extracting and canceling out 16.

$$\frac{14023731676575669}{9559765268913809}$$

Factor

$$\frac{3 \cdot 4674577225525223}{223 \cdot 70769 \cdot 605758207} = 1\frac{4463966407661860}{9559765268913808} = 1.4669535581775912$$