9. The value of log sin1'. log sin2.... log sin 179. is
a) 1
b)2
C
c)sin 90°
do
Answers
Step-by-step explanation:
The given expression is
\log \sin 1\cdot \log \sin 2\cdot \log \sin 3\cdot...\cdot\log \sin 179logsin1⋅logsin2⋅logsin3⋅...⋅logsin179
We need to find the value of given expression.
From the given expression it is clear that \log \sin 90logsin90 term of lies in the expression.
We know that
\sin 90^{\circ}=1sin90
∘
=1
\log(1)=0log(1)=0
Using this facts, we get
\log \sin 90=\log (1)=0logsin90=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 179logsin1⋅logsin2⋅logsin3⋅...⋅logsin90⋅...⋅logsin179
\log \sin 1\cdot \log \sin 2\cdot \log \sin 3\cdot...\cdot (0) \cdot...\cdot\log \sin 179logsin1⋅logsin2⋅logsin3⋅...⋅(0)⋅...⋅logsin179
00
Therefore, the value of given expression is 0.