Solve 2sin40^circcos40/cos10^circ

$$\frac { 2 \sin 40 ^ { \circ } \cos 40 } { \cos 10 ^ { \circ } }$$

Evaluate

$$\frac{2462019382530519934456974864177}{2462019382530520000000000000000}\approx 1$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{2 \cdot 0.6427876096865393 \cdot 0.766044443118978}{0.984807753012208}$$

Multiply 2 and 0.6427876096865393 to get 1.2855752193730786.

$$\frac{1.2855752193730786\times 0.766044443118978}{0.984807753012208}$$

Multiply 1.2855752193730786 and 0.766044443118978 to get 0.9848077530122079737827899456708.

$$\frac{0.9848077530122079737827899456708}{0.984807753012208}$$

Expand \frac{0.9848077530122079737827899456708}{0.984807753012208} by multiplying both numerator and the denominator by 10000000000000000000000000000000.

$$\frac{9848077530122079737827899456708}{9848077530122080000000000000000}$$

Reduce the fraction \frac{9848077530122079737827899456708}{9848077530122080000000000000000} to lowest terms by extracting and canceling out 4.

$$\frac{2462019382530519934456974864177}{2462019382530520000000000000000}$$