<s>[INST] How to calculate $\left( 1+\tan 5^\circ\right) \left( 1+\tan 10^\circ\right)\left( 1+\tan 15^\circ\right)\cdots\left( 1+\tan 40^\circ\right)$ I curious practical solution.(Step by step) 
$\left( 1+\tan 5^\circ\right) \left( 1+\tan 10^\circ\right)\left( 1+\tan 15^\circ\right)\cdots\left( 1+\tan 40^\circ\right)$   
Answer is $16$.
 [/INST] If $\displaystyle A+B = \frac{\pi}{4}\;,$ Then $(1+\tan A)(1+\tan B) = 2$
So $(1+\tan 5^0)(1+\tan 40^0)=2$ and $(1+\tan 10^0)(1+\tan 35^0)=2$
and $(1+\tan 15^0)(1+\tan 30^0)=2$ and $(1+\tan 20^0)(1+\tan 35^0)=2$
So $$(1+\tan 5^0)(1+\tan 40^0)(1+\tan 10^0)(1+\tan 35^0)(1+\tan 15^0)(1+\tan 30^0)(1+\tan 20^0)(1+\tan 35^0)=2^4=16$$
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