Answers

2015-04-22T00:39:01+05:30
Recall the identity \tan(90-\theta)=\cot(\theta) noticing that 65=90-25 and 75=90-15 :

\tan(15)\tan(25)\tan(60)\tan(65)\tan(75)\\=\tan(15)\tan(25)\tan(60)\tan(90-25)\tan(90-15)\\=\tan(15)\tan(25)\tan(60)\cot(25)\cot(15)\\=\tan(15)\cot(15)\tan(25)\cot(25)\tan(60)\\=\tan(60)\\=\sqrt{3}
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2015-04-22T10:01:39+05:30
tan15tan25tan60tan65tan75

=tan(90-75)tan(90-65)tan60tan65tan75

=cot 75cot65tan60tan65tan75

cot75-tan75 and cot 65-tan65 both cancelled

=tan60

= \sqrt{3}
                                                                 hope you understood
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