Resolver frac{sin31^{circ}sin29^{circ}+cot39^circcot3}{8sin^230-tan^245^circ}

$$\frac { \sin 31 ^ { \circ } \sin 29 ^ { \circ } + \cot 39 ^ { \circ } \cot 3 } { 8 \sin ^ { 2 } 30 - \tan ^ { 2 } 45 ^ { \circ } }$$

Avaliar

$$23,812936852641771486973359544141152$$

Passos Para a Resolução

Evaluate trigonometric functions in the problem

$$\frac{0,5150380749100542 \cdot 0,48480962024633706 + 1,2348971565350515 \cdot 19,081136687728215}{8 \sin^{2}(30) - \tan^{2}(45)}$$

Multiplique 0,5150380749100542 e 0,48480962024633706 para obter 0,249695413509547876042806516068652.

$$\frac{0,249695413509547876042806516068652+1,2348971565350515\times 19,081136687728215}{8\left(\sin(30)\right)^{2}-\left(\tan(45)\right)^{2}}$$

Multiplique 1,2348971565350515 e 19,081136687728215 para obter 23,5632414391322236109305530280725.

$$\frac{0,249695413509547876042806516068652+23,5632414391322236109305530280725}{8\left(\sin(30)\right)^{2}-\left(\tan(45)\right)^{2}}$$

Some 0,249695413509547876042806516068652 e 23,5632414391322236109305530280725 para obter 23,812936852641771486973359544141152.

$$\frac{23,812936852641771486973359544141152}{8\left(\sin(30)\right)^{2}-\left(\tan(45)\right)^{2}}$$

Obtenha o valor de \sin(30) a partir da tabela de valores trigonométricos.

$$\frac{23,812936852641771486973359544141152}{8\times \left(\frac{1}{2}\right)^{2}-\left(\tan(45)\right)^{2}}$$

Calcule \frac{1}{2} elevado a 2 e obtenha \frac{1}{4}.

$$\frac{23,812936852641771486973359544141152}{8\times \frac{1}{4}-\left(\tan(45)\right)^{2}}$$

Multiplique 8 e \frac{1}{4} para obter 2.

$$\frac{23,812936852641771486973359544141152}{2-\left(\tan(45)\right)^{2}}$$

Obtenha o valor de \tan(45) a partir da tabela de valores trigonométricos.

$$\frac{23,812936852641771486973359544141152}{2-1^{2}}$$

Calcule 1 elevado a 2 e obtenha 1.

$$\frac{23,812936852641771486973359544141152}{2-1}$$

Subtraia 1 de 2 para obter 1.

$$\frac{23,812936852641771486973359544141152}{1}$$

Qualquer número dividido por um resulta no próprio número.

$$23,812936852641771486973359544141152$$