Solve frac{cos11^{circ}+2sin11^circ}{cos11^circ-sin11^circ}=tan56^circ

$$\frac { \cos 11 ^ { \circ } + 2 \sin 11 ^ { \circ } } { \cos 11 ^ { \circ } - \sin 11 ^ { \circ } } = \tan 56 ^ { \circ }$$

Verify

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.981627183447664 + 2 \cdot 0.1908089953765448}{0.981627183447664 - 0.1908089953765448} = 1.4825609685127403$$

Multiply 2 and 0.1908089953765448 to get 0.3816179907530896.

$$\frac{0.981627183447664+0.3816179907530896}{0.981627183447664-0.1908089953765448}=1.4825609685127403$$

Add 0.981627183447664 and 0.3816179907530896 to get 1.3632451742007536.

$$\frac{1.3632451742007536}{0.981627183447664-0.1908089953765448}=1.4825609685127403$$

Subtract 0.1908089953765448 from 0.981627183447664 to get 0.7908181880711192.

$$\frac{1.3632451742007536}{0.7908181880711192}=1.4825609685127403$$

Expand \frac{1.3632451742007536}{0.7908181880711192} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{13632451742007536}{7908181880711192}=1.4825609685127403$$

Reduce the fraction \frac{13632451742007536}{7908181880711192} to lowest terms by extracting and canceling out 8.

$$\frac{1704056467750942}{988522735088899}=1.4825609685127403$$

Convert decimal number 1.4825609685127403 to fraction \frac{14825609685127403}{10000000000}. Reduce the fraction \frac{14825609685127403}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{1704056467750942}{988522735088899}=\frac{14825609685127403}{10000000000000000}$$

Least common multiple of 988522735088899 and 10000000000000000 is 9885227350888990000000000000000. Convert \frac{1704056467750942}{988522735088899} and \frac{14825609685127403}{10000000000000000} to fractions with denominator 9885227350888990000000000000000.

$$\frac{17040564677509420000000000000000}{9885227350888990000000000000000}=\frac{14655452235302611112405345999297}{9885227350888990000000000000000}$$

Compare \frac{17040564677509420000000000000000}{9885227350888990000000000000000} and \frac{14655452235302611112405345999297}{9885227350888990000000000000000}.

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