Solve cos7^circ-sin15^circsin8^circ/cos8^circ

$$\frac { \cos 7 ^ { \circ } - \sin 15 ^ { \circ } \sin 8 ^ { \circ } } { \cos 8 ^ { \circ } }$$

Evaluate

$$\frac{298914219545900359494742056450867}{309458771481740750000000000000000}\approx 0.965925826$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.992546151641322 - 0.25881904510252074 \cdot 0.13917310096006544}{0.9902680687415704}$$

Multiply 0.25881904510252074 and 0.13917310096006544 to get 0.0360206490944408496168254193572256.

$$\frac{0.992546151641322-0.0360206490944408496168254193572256}{0.9902680687415704}$$

Subtract 0.0360206490944408496168254193572256 from 0.992546151641322 to get 0.9565255025468811503831745806427744.

$$\frac{0.9565255025468811503831745806427744}{0.9902680687415704}$$

Expand \frac{0.9565255025468811503831745806427744}{0.9902680687415704} by multiplying both numerator and the denominator by 10000000000000000000000000000000000.

$$\frac{9565255025468811503831745806427744}{9902680687415704000000000000000000}$$

Reduce the fraction \frac{9565255025468811503831745806427744}{9902680687415704000000000000000000} to lowest terms by extracting and canceling out 32.

$$\frac{298914219545900359494742056450867}{309458771481740750000000000000000}$$

Factor

$$\frac{3 \cdot 11 \cdot 31 \cdot 541 \cdot 10067 \cdot 53650479494773198568107}{17 \cdot 85717 \cdot 849467767 \cdot 2 ^ {16} \cdot 5 ^ {18}} = 0.9659258262890681$$