Solve frac{4sin17^{circ}cos17^{circ}(2cos51^{circ}cos17^circ-sin34^circ)}{sin104^circ-sin34^circ}

$$\frac { 4 \sin 17 ^ { \circ } \cos 17 ^ { \circ } ( 2 \cos 51 ^ { \circ } \cos 17 ^ { \circ } - \sin 34 ^ { \circ } ) } { \sin 104 ^ { \circ } - \sin 34 ^ { \circ } }$$

Evaluate

$$\frac{143521544234982071675548455745869}{51387852850656200000000000000000}\approx 2.792907979$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{4 \cdot 0.29237170472273677 \cdot 0.9817745145419394}{0.9702957262759965 - 0.5591929034707469}$$

Multiply 4 and 0.29237170472273677 to get 1.16948681889094708.

$$\frac{1.16948681889094708\times 0.9817745145419394}{0.9702957262759965-0.5591929034707469}$$

Multiply 1.16948681889094708 and 0.9817745145419394 to get 1.148172353879856573404387645966952.

$$\frac{1.148172353879856573404387645966952}{0.9702957262759965-0.5591929034707469}$$

Subtract 0.5591929034707469 from 0.9702957262759965 to get 0.4111028228052496.

$$\frac{1.148172353879856573404387645966952}{0.4111028228052496}$$

Expand \frac{1.148172353879856573404387645966952}{0.4111028228052496} by multiplying both numerator and the denominator by 1000000000000000000000000000000000.

$$\frac{1148172353879856573404387645966952}{411102822805249600000000000000000}$$

Reduce the fraction \frac{1148172353879856573404387645966952}{411102822805249600000000000000000} to lowest terms by extracting and canceling out 8.

$$\frac{143521544234982071675548455745869}{51387852850656200000000000000000}$$