Solve 30^{circ}+frac{sin31^{circ}sec59^{circ}+cot59^{circ}cot31^{circ}}{8sin^230^circ-tan^245^circ}

$$30 ^ { \circ } + \frac { \sin 31 ^ { \circ } \sec 59 ^ { \circ } + \cot 59 ^ { \circ } \cot 31 ^ { \circ } } { 8 \sin ^ { 2 } 30 ^ { \circ } - \tan ^ { 2 } 45 ^ { \circ } }$$

Evaluate

$$32.00000000000000025142552606969684$$

Solution Steps

Evaluate trigonometric functions in the problem

$$30 + \frac{0.5150380749100542 \cdot 1.9416040264103562 + 0.6008606190275606 \cdot 1.664279482350518}{8 \sin^{2}(30) - \tan^{2}(45)}$$

Multiply 0.5150380749100542 and 1.9416040264103562 to get 0.99999999999999988987361438330604.

$$30+\frac{0.99999999999999988987361438330604+0.6008606190275606\times 1.664279482350518}{8\left(\sin(30)\right)^{2}-\left(\tan(45)\right)^{2}}$$

Multiply 0.6008606190275606 and 1.664279482350518 to get 1.0000000000000003615519116863908.

$$30+\frac{0.99999999999999988987361438330604+1.0000000000000003615519116863908}{8\left(\sin(30)\right)^{2}-\left(\tan(45)\right)^{2}}$$

Add 0.99999999999999988987361438330604 and 1.0000000000000003615519116863908 to get 2.00000000000000025142552606969684.

$$30+\frac{2.00000000000000025142552606969684}{8\left(\sin(30)\right)^{2}-\left(\tan(45)\right)^{2}}$$

Get the value of \sin(30) from trigonometric values table.

$$30+\frac{2.00000000000000025142552606969684}{8\times \left(\frac{1}{2}\right)^{2}-\left(\tan(45)\right)^{2}}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$30+\frac{2.00000000000000025142552606969684}{8\times \frac{1}{4}-\left(\tan(45)\right)^{2}}$$

Multiply 8 and \frac{1}{4} to get 2.

$$30+\frac{2.00000000000000025142552606969684}{2-\left(\tan(45)\right)^{2}}$$

Get the value of \tan(45) from trigonometric values table.

$$30+\frac{2.00000000000000025142552606969684}{2-1^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$30+\frac{2.00000000000000025142552606969684}{2-1}$$

Subtract 1 from 2 to get 1.

$$30+\frac{2.00000000000000025142552606969684}{1}$$

Anything divided by one gives itself.

$$30+2.00000000000000025142552606969684$$

Add 30 and 2.00000000000000025142552606969684 to get 32.00000000000000025142552606969684.

$$32.00000000000000025142552606969684$$