Solve (1+tan(33))(1+tan(12))*1/(1+tan(18))(1+tan(27))

$$(1+ \tan ( 33 ) )(1+ \tan ( 12 ) ) \times \frac{ 1 }{ (1+ \tan ( 18 ) )(1+ \tan ( 27 ) ) }$$

Evaluate

$$\frac{14285714285714285616051345478459}{14285714285714285332765922017296}\approx 1$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(1 + 0.6494075931975106)} {(1 + 0.2125565616700221)} \cdot \frac{1}{{(1 + 0.3249196962329063)} {(1 + 0.5095254494944288)}}$$

Add 1 and 0.6494075931975106 to get 1.6494075931975106.

$$1.6494075931975106\left(1+0.2125565616700221\right)\times \frac{1}{\left(1+0.3249196962329063\right)\left(1+0.5095254494944288\right)}$$

Add 1 and 0.2125565616700221 to get 1.2125565616700221.

$$1.6494075931975106\times 1.2125565616700221\times \frac{1}{\left(1+0.3249196962329063\right)\left(1+0.5095254494944288\right)}$$

Multiply 1.6494075931975106 and 1.2125565616700221 to get 1.99999999999999998624718836698426.

$$1.99999999999999998624718836698426\times \frac{1}{\left(1+0.3249196962329063\right)\left(1+0.5095254494944288\right)}$$

Add 1 and 0.3249196962329063 to get 1.3249196962329063.

$$1.99999999999999998624718836698426\times \frac{1}{1.3249196962329063\left(1+0.5095254494944288\right)}$$

Add 1 and 0.5095254494944288 to get 1.5095254494944288.

$$1.99999999999999998624718836698426\times \frac{1}{1.3249196962329063\times 1.5095254494944288}$$

Multiply 1.3249196962329063 and 1.5095254494944288 to get 1.99999999999999994658722908242144.

$$1.99999999999999998624718836698426\times \frac{1}{1.99999999999999994658722908242144}$$

Expand \frac{1}{1.99999999999999994658722908242144} by multiplying both numerator and the denominator by 100000000000000000000000000000000.

$$1.99999999999999998624718836698426\times \frac{100000000000000000000000000000000}{199999999999999994658722908242144}$$

Reduce the fraction \frac{100000000000000000000000000000000}{199999999999999994658722908242144} to lowest terms by extracting and canceling out 32.

$$1.99999999999999998624718836698426\times \frac{3125000000000000000000000000000}{6249999999999999833085090882567}$$

Convert decimal number 1.99999999999999998624718836698426 to fraction \frac{99999999999999999312359418349213}{10000000000}. Reduce the fraction \frac{99999999999999999312359418349213}{10000000000} to lowest terms by extracting and canceling out 1.

$$\frac{99999999999999999312359418349213}{50000000000000000000000000000000}\times \frac{3125000000000000000000000000000}{6249999999999999833085090882567}$$

Multiply \frac{99999999999999999312359418349213}{50000000000000000000000000000000} times \frac{3125000000000000000000000000000}{6249999999999999833085090882567} by multiplying numerator times numerator and denominator times denominator.

$$\frac{99999999999999999312359418349213\times 3125000000000000000000000000000}{50000000000000000000000000000000\times 6249999999999999833085090882567}$$

Do the multiplications in the fraction \frac{99999999999999999312359418349213\times 3125000000000000000000000000000}{50000000000000000000000000000000\times 6249999999999999833085090882567}.

$$\frac{312499999999999997851123182341290625000000000000000000000000000}{312499999999999991654254544128350000000000000000000000000000000}$$

Reduce the fraction \frac{312499999999999997851123182341290625000000000000000000000000000}{312499999999999991654254544128350000000000000000000000000000000} to lowest terms by extracting and canceling out 21875000000000000000000000000000.

$$\frac{14285714285714285616051345478459}{14285714285714285332765922017296}$$

Factor

$$\frac{17 \cdot 419 \cdot 7411 \cdot 93487 \cdot 557844467 \cdot 5189169407}{3 \cdot 47 \cdot 21179 \cdot 22769 \cdot 25253 \cdot 126001 \cdot 4126924147 \cdot 2 ^ {4}} = 1$$