What will be the value of expression log cot 9° + log cot 45° + log cot 81°?
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
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