Question

log( tan 30°)+log( tan 60°)

Answer 1

hope it helps................

Answer 2

$\displaystyle \sf{log(tan {30}^{ \circ}) + log(tan {60}^{ \circ}) } = \bf \: 0$

Given :

$\displaystyle \sf{log(tan {30}^{ \circ}) + log(tan {60}^{ \circ}) }$

To find :

Simplify the expression

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf{log(tan {30}^{ \circ}) + log(tan {60}^{ \circ}) }$

Step 2 of 2 :

Simplify the given expression

$\displaystyle \sf{log(tan {30}^{ \circ}) + log(tan {60}^{ \circ}) }$

$\displaystyle \sf{ = log(tan {30}^{ \circ} \times tan {60}^{ \circ}) \: \: \: \bigg[ \: \because \:log \: a + log \: b = log \: (ab) \bigg] }$

$\displaystyle \sf{ = log\: \bigg( \frac{1}{ \sqrt{3} } \times \sqrt{3} \bigg) }$

$\displaystyle \sf{ = log\: 1 }$

$= 0$

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