Solve sin43^circcos13^circ-cos42^circsin13^circ=

$$\sin 43 ^ { \circ } \cos 13 ^ { \circ } - \cos 42 ^ { \circ } \sin 13 ^ { \circ } =$$

Evaluate

$$0.4973475742561934522319810655642$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.6819983600624985 \cdot 0.9743700647852352 - 0.7431448254773942 \cdot 0.224951054343865$$

Multiply 0.6819983600624985 and 0.9743700647852352 to get 0.6645187862775208261082520221472.

$$0.6645187862775208261082520221472-0.7431448254773942\times 0.224951054343865$$

Multiply 0.7431448254773942 and 0.224951054343865 to get 0.167171212021327373876270956583.

$$0.6645187862775208261082520221472-0.167171212021327373876270956583$$

Subtract 0.167171212021327373876270956583 from 0.6645187862775208261082520221472 to get 0.4973475742561934522319810655642.

$$0.4973475742561934522319810655642$$

Factor

$$\frac{7 \cdot 101 \cdot 3517309577483687780989965103}{2 ^ {30} \cdot 5 ^ {31}} = 0.49734757425619347$$