Solve 2sin67/cos23+tan40/cot50+cos0

$$\frac { 2 \sin 67 } { \cos 23 } + \frac { \tan 40 } { \cot 50 } + \cos 0$$

Evaluate

$$\frac{77239528302883885114193813893699}{19309882075720972902738525852800}\approx 4$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{2 \cdot 0.9205048534524403}{0.9205048534524404} + \frac{0.8390996311772799}{0.83909963117728} + \cos(0)$$

Multiply 2 and 0.9205048534524403 to get 1.8410097069048806.

$$\frac{1.8410097069048806}{0.9205048534524404}+\frac{0.8390996311772799}{0.83909963117728}+\cos(0)$$

Expand \frac{1.8410097069048806}{0.9205048534524404} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{18410097069048806}{9205048534524404}+\frac{0.8390996311772799}{0.83909963117728}+\cos(0)$$

Reduce the fraction \frac{18410097069048806}{9205048534524404} to lowest terms by extracting and canceling out 2.

$$\frac{9205048534524403}{4602524267262202}+\frac{0.8390996311772799}{0.83909963117728}+\cos(0)$$

Expand \frac{0.8390996311772799}{0.83909963117728} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{9205048534524403}{4602524267262202}+\frac{8390996311772799}{8390996311772800}+\cos(0)$$

Add \frac{9205048534524403}{4602524267262202} and \frac{8390996311772799}{8390996311772800} to get \frac{57929646227162912211455288040899}{19309882075720972902738525852800}.

$$\frac{57929646227162912211455288040899}{19309882075720972902738525852800}+\cos(0)$$

Get the value of \cos(0) from trigonometric values table.

$$\frac{57929646227162912211455288040899}{19309882075720972902738525852800}+1$$

Add \frac{57929646227162912211455288040899}{19309882075720972902738525852800} and 1 to get \frac{77239528302883885114193813893699}{19309882075720972902738525852800}.

$$\frac{77239528302883885114193813893699}{19309882075720972902738525852800}$$