Log sin 1 . log sin 2 . log sin 3 .............log sin 179 – InterviewSolution

1.

Log sin 1 . log sin 2 . log sin 3 .............log sin 179

Answer»

Answer:

0

Step-by-step explanation:

The given expression is

$\log \sin 1\cdot \log \sin 2\cdot \log \sin 3\cdot...\cdot\log \sin 179$

We NEED to find the VALUE of given expression.

From the given expression it is clear that $\log \sin 90$ TERM of LIES in the expression.

We know that

$\sin 90^{\circ}=1$

$\log(1)=0$

Using this facts, we get

$\log \sin 90=\log (1)=0$

If any NUMBER multiplied by 0, then the resultant value is 0.

$\log \sin 1\cdot \log \sin 2\cdot \log \sin 3\cdot...\cdot \log \sin 90\cdot...\cdot\log \sin 179$

$\log \sin 1\cdot \log \sin 2\cdot \log \sin 3\cdot...\cdot (0) \cdot...\cdot\log \sin 179$

$0$

Therefore, the value of given expression is 0.

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