Solve 2cos^29.42/sin(2*17.47)

$$\frac { 2 \cos ^ { 2 } 9.42 } { \sin ( 2 \cdot 17.47 ) }$$

Evaluate

$$\frac{249142277829552323712364521}{73307943423302067200000000}\approx 3.398571372$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{2 \cdot 0.9865150899868125 ^ {2}}{0.5727183079945474}$$

Calculate 0.9865150899868125 to the power of 2 and get 0.97321202277168876450142391015625.

$$\frac{2\times 0.97321202277168876450142391015625}{0.5727183079945474}$$

Multiply 2 and 0.97321202277168876450142391015625 to get 1.9464240455433775290028478203125.

$$\frac{1.9464240455433775290028478203125}{0.5727183079945474}$$

Expand \frac{1.9464240455433775290028478203125}{0.5727183079945474} by multiplying both numerator and the denominator by 10000000000000000000000000000000.

$$\frac{19464240455433775290028478203125}{5727183079945474000000000000000}$$

Reduce the fraction \frac{19464240455433775290028478203125}{5727183079945474000000000000000} to lowest terms by extracting and canceling out 78125.

$$\frac{249142277829552323712364521}{73307943423302067200000000}$$

Factor

$$\frac{3 ^ {8} \cdot 254083 ^ {2} \cdot 766943 ^ {2}}{58440643672913 \cdot 2 ^ {16} \cdot 5 ^ {8} \cdot 7 ^ {2}} = 3\frac{2.9218447559646132 \times 10^{25}}{7.330794342330205 \times 10^{25}} = 3.398571371603348$$