Solve frac{sin24^{circ}cos6^{circ}-sin6^{circ}sin66^{circ}}{sin21^circcos39^circ-cos51^circsin69^circ}

$$\frac { \sin 24 ^ { \circ } \cos 6 ^ { \circ } - \sin 6 ^ { \circ } \sin 66 ^ { \circ } } { \sin 21 ^ { \circ } \cos 39 ^ { \circ } - \cos 51 ^ { \circ } \sin 69 ^ { \circ } }$$

Evaluate

$$-\frac{309016994374947361590989047096881}{309016994374947432957839064571607}\approx -1$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.40673664307580015 \cdot 0.9945218953682733 - 0.10452846326765346 \cdot 0.9135454576426009}{0.35836794954530027 \cdot 0.7771459614569709 - 0.6293203910498375 \cdot 0.9335804264972017}$$

Multiply 0.40673664307580015 and 0.9945218953682733 to get 0.404508497187473639595731321380995.

$$\frac{0.404508497187473639595731321380995-0.10452846326765346\times 0.9135454576426009}{0.35836794954530027\times 0.7771459614569709-0.6293203910498375\times 0.9335804264972017}$$

Multiply 0.10452846326765346 and 0.9135454576426009 to get 0.095491502812526278004742274284114.

$$\frac{0.404508497187473639595731321380995-0.095491502812526278004742274284114}{0.35836794954530027\times 0.7771459614569709-0.6293203910498375\times 0.9335804264972017}$$

Subtract 0.095491502812526278004742274284114 from 0.404508497187473639595731321380995 to get 0.309016994374947361590989047096881.

$$\frac{0.309016994374947361590989047096881}{0.35836794954530027\times 0.7771459614569709-0.6293203910498375\times 0.9335804264972017}$$

Multiply 0.35836794954530027 and 0.7771459614569709 to get 0.278504204704745615797579925152143.

$$\frac{0.309016994374947361590989047096881}{0.278504204704745615797579925152143-0.6293203910498375\times 0.9335804264972017}$$

Multiply 0.6293203910498375 and 0.9335804264972017 to get 0.58752119907969304875541898972375.

$$\frac{0.309016994374947361590989047096881}{0.278504204704745615797579925152143-0.58752119907969304875541898972375}$$

Subtract 0.58752119907969304875541898972375 from 0.278504204704745615797579925152143 to get -0.309016994374947432957839064571607.

$$\frac{0.309016994374947361590989047096881}{-0.309016994374947432957839064571607}$$

Expand \frac{0.309016994374947361590989047096881}{-0.309016994374947432957839064571607} by multiplying both numerator and the denominator by 1000000000000000000000000000000000.

$$\frac{309016994374947361590989047096881}{-309016994374947432957839064571607}$$

Fraction \frac{309016994374947361590989047096881}{-309016994374947432957839064571607} can be rewritten as -\frac{309016994374947361590989047096881}{309016994374947432957839064571607} by extracting the negative sign.

$$-\frac{309016994374947361590989047096881}{309016994374947432957839064571607}$$

Factor

$$-\frac{309016994374947361590989047096881}{309016994374947432957839064571607} = -0.9999999999999998$$