Solve F=sin9^circcos39^circ-cos9^circsin39^circ/cosfrac{3pi{7}*cos5pi/25-sin3pi/7sin5pi/28}

$$F = \frac { \sin 9 ^ { \circ } \cos 39 ^ { \circ } - \cos 9 ^ { \circ } \sin 39 ^ { \circ } } { \cos \frac { 3 \pi } { 7 } \cdot \cos \frac { 5 \pi } { 25 } - \sin \frac { 3 \pi } { 7 } \sin \frac { 5 \pi } { 28 } }$$

Solve for F

$$F = \frac{499999999999999990491987013722037}{55549746464456134882673155823760} = 9\frac{5.228181989472565 \times 10^{28}}{5.554974646445614 \times 10^{31}} \approx 9.000941171$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$F = \frac{0.15643446504023087 \cdot 0.7771459614569709 - 0.9876883405951378 \cdot 0.6293203910498374}{0.4631431751064012 - 0.9749279121818236 \cdot 0.5320320765153366}$$

Multiply 0.15643446504023087 and 0.7771459614569709 to get 0.121572412738697121408468906871683.

$$F=\frac{0.121572412738697121408468906871683-0.9876883405951378\times 0.6293203910498374}{0.4631431751064012-0.9749279121818236\times 0.5320320765153366}$$

Multiply 0.9876883405951378 and 0.6293203910498374 to get 0.62157241273869711190045592059372.

$$F=\frac{0.121572412738697121408468906871683-0.62157241273869711190045592059372}{0.4631431751064012-0.9749279121818236\times 0.5320320765153366}$$

Subtract 0.62157241273869711190045592059372 from 0.121572412738697121408468906871683 to get -0.499999999999999990491987013722037.

$$F=\frac{-0.499999999999999990491987013722037}{0.4631431751064012-0.9749279121818236\times 0.5320320765153366}$$

Multiply 0.9749279121818236 and 0.5320320765153366 to get 0.51869292157085733488267315582376.

$$F=\frac{-0.499999999999999990491987013722037}{0.4631431751064012-0.51869292157085733488267315582376}$$

Subtract 0.51869292157085733488267315582376 from 0.4631431751064012 to get -0.05554974646445613488267315582376.

$$F=\frac{-0.499999999999999990491987013722037}{-0.05554974646445613488267315582376}$$

Expand \frac{-0.499999999999999990491987013722037}{-0.05554974646445613488267315582376} by multiplying both numerator and the denominator by 1000000000000000000000000000000000.

$$F=\frac{-499999999999999990491987013722037}{-55549746464456134882673155823760}$$

Fraction \frac{-499999999999999990491987013722037}{-55549746464456134882673155823760} can be simplified to \frac{499999999999999990491987013722037}{55549746464456134882673155823760} by removing the negative sign from both the numerator and the denominator.

$$F=\frac{499999999999999990491987013722037}{55549746464456134882673155823760}$$

Assign F

$$F≔\frac{499999999999999990491987013722037}{55549746464456134882673155823760}$$