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Can you please give a hint how to solve this exercise:

$$\log(\tan 22)+ \log(\tan 68)=?\\ \tan22\cdot\tan68=?$$

Thank you!

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Another hint: for this problem in particular you could have worked it out numerically with a calculator; that's not sufficient to give a justification for the answer but the justification is easier to come up with if you know the answer. –  Eric Lippert Mar 29 at 14:50
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Yes, that's a good hint but imagine I have an exam and don't have a calculator:) –  John G. Mar 29 at 14:52

2 Answers 2

up vote 4 down vote accepted

Hint In degree $$\tan(90-x)=\frac{1}{\tan x}$$

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Sami Ben Romdhane@ Thanks!!! –  John G. Mar 29 at 13:49
    
You're welcome. –  Sami Ben Romdhane Mar 29 at 13:51

HINT:

$$22^\circ=90^\circ-68^\circ$$ and $$\tan(90^\circ-x)=\cot x$$

also $$\tan22^\circ\cdot\tan68^\circ\ne0$$

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Thank you for this hint –  John G. Mar 29 at 13:48

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