The value of log(sin 1^{circ}) cdot log(sin 2 | vedclass

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Question

(D) The given expression is $P = \log(\sin 1^{\circ}) \cdot \log(\sin 2^{\circ}) \cdot \dots \cdot \log(\sin 90^{\circ}) \cdot \dots \cdot \log(\sin 1

Vedclass · Accepted Answer

is zero

Vedclass · Answer

(D) The given expression is $P = \log(\sin 1^{\circ}) \cdot \log(\sin 2^{\circ}) \cdot \dots \cdot \log(\sin 90^{\circ}) \cdot \dots \cdot \log(\sin 179^{\circ})$.We know that $\sin 90^{\circ} = 1$.Therefore,the term $\log(\sin 90^{\circ}) = \log(1) = 0$.Since the expression is a product of terms including $\log(\sin 90^{\circ})$,the entire product becomes $0$ because any number multiplied by $0$ is $0$.Thus,the value is $0$.

The value of $\log(\sin 1^{\circ}) \cdot \log(\sin 2^{\circ}) \cdot \log(\sin 3^{\circ}) \dots \log(\sin 179^{\circ})$ is:

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