Solve frac{cos^{2}50^{circ}*cos^240^circ+1}{cos^240^circ}

$$\frac { \cos ^ { 2 } 50 ^ { \circ } \cdot \cos ^ { 2 } 40 ^ { \circ } + 1 } { \cos ^ { 2 } 40 ^ { \circ } }$$

Evaluate

$$\frac{175989071291081761708225746656321}{58682408883346512049266376448400}\approx 2.999008981$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.8717171060102111 ^ {2} + 1}{0.766044443118978 ^ {2}}$$

Calculate 0.8717171060102111 to the power of 2 and get 0.75989071291081761708225746656321.

$$\frac{0.75989071291081761708225746656321+1}{0.766044443118978^{2}}$$

Add 0.75989071291081761708225746656321 and 1 to get 1.75989071291081761708225746656321.

$$\frac{1.75989071291081761708225746656321}{0.766044443118978^{2}}$$

Calculate 0.766044443118978 to the power of 2 and get 0.586824088833465120492663764484.

$$\frac{1.75989071291081761708225746656321}{0.586824088833465120492663764484}$$

Expand \frac{1.75989071291081761708225746656321}{0.586824088833465120492663764484} by multiplying both numerator and the denominator by 100000000000000000000000000000000.

$$\frac{175989071291081761708225746656321}{58682408883346512049266376448400}$$