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