Question

tan 7° tan 23° tan 60° tan 67° tan 83° + $\frac{\cot 54°}{\tan 36°}$ + sin 20° sec 70° − 2

Answer 1

$$\begin{gathered} \begin{array}{l}{\text{tan7}}^0\tan {23}^0\tan {60}^0\tan {67}^0\tan {83}^0+\frac{\cot {54}^0}{\tan {36}^0}+\sin {20}^0\sec {70}^0-2\\ \end{array} \\ \begin{array}{l}=\left(\tan {60}^0\right)\left(\tan 7^0\tan {83}^0\right)\left(\tan {23}^0\tan {67}^0\right)+\frac{\cot ({90}^0-{36}^0)}{\tan {36}^0}+\sin {20}^0\sec ({90}^0-{20}^0)-2\\ \end{array} \\ \begin{array}{l}\text{=}\sqrt{3}\left\{\tan 7^0\tan ({90}^0-7^0)\right\}\left\{\tan {23}^0\tan ({90}^0-{23}^0)\right\}+\frac{\tan {36}^0}{\tan {36}^0}+\sin {20}^0\cos \text{ec}{20}^0-2\\ \end{array} \\ \begin{array}{l}\text{=}\sqrt{3}\left(\tan 7^0\cot 7^0\right)\left(\tan {23}^0\cot {23}^0\right)+1+\sin {20}^0\frac{1}{\sin {20}^0}-2\\ \end{array} \\ \begin{array}{l}=\sqrt{3}\times (1\times 1)+1+1-2\\ \end{array} \\ \begin{array}{l}\text{=}\sqrt{3}\times 1\\ \end{array} \\ \text{=}\sqrt{3} \end{gathered}$$