Solve 56^{circ}=cos11^circ+sin11^circ/cos11^circ-sin11^circ

$$56 ^ { \circ } = \frac { \cos 11 ^ { \circ } + \sin 11 ^ { \circ } } { \cos 11 ^ { \circ } - \sin 11 ^ { \circ } }$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$56 = \frac{0.981627183447664 + 0.1908089953765448}{0.981627183447664 - 0.1908089953765448}$$

Add 0.981627183447664 and 0.1908089953765448 to get 1.1724361788242088.

$$56=\frac{1.1724361788242088}{0.981627183447664-0.1908089953765448}$$

Subtract 0.1908089953765448 from 0.981627183447664 to get 0.7908181880711192.

$$56=\frac{1.1724361788242088}{0.7908181880711192}$$

Expand \frac{1.1724361788242088}{0.7908181880711192} by multiplying both numerator and the denominator by 10000000000000000.

$$56=\frac{11724361788242088}{7908181880711192}$$

Reduce the fraction \frac{11724361788242088}{7908181880711192} to lowest terms by extracting and canceling out 8.

$$56=\frac{1465545223530261}{988522735088899}$$

Convert 56 to fraction \frac{55357273164978344}{988522735088899}.

$$\frac{55357273164978344}{988522735088899}=\frac{1465545223530261}{988522735088899}$$

Compare \frac{55357273164978344}{988522735088899} and \frac{1465545223530261}{988522735088899}.

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