1.

What will be the value of expression log cot 9° + log cot 45° + log cot 81°?

Answer» Correct Answer - Option 1 : 0

Given:

The given logarithmic expression is log cot 9° + log cot 45° + log cot 81°?

Formula Used:

Basic concept of trigonometric ratio and identities

We know that

log m + log n = log (m × n)

tan θ = cot (90 - θ)

tan θ × cot θ = 1

cot 45° = 1

log 1 = 0

Calculation:

By applying the identity of log

∴ log cot 9° + log cot 45° + log cot 81° = log ( cot 9° × cot 45° × cot 81°)

⇒ log ( cot 9° × cot 45° × cot 81°) = log ( cot 9° × cot 45° × cot (90 - 9)°)

⇒ log ( cot 9° × cot 45° × tan 9°) = log 1 = 0

Hence, option (1) is correct



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