log-tan-x-sinx-1-log-cos-x-tanx-

Question Number 207128 by hardmath last updated on 07/May/24

\log_{\tan x} sinx - \frac{1}{\log_{\cos x} tanx} = ?

Answered by Frix last updated on 07/May/24

= \frac{\ln s}{\ln t} - \frac{\ln c}{\ln t} = \frac{\ln s - \ln c}{\ln \frac{s}{c}}

If c > 0 \land s > 0 this is equal to 1, else {it}^{'} s getting

complicated .

Commented by hardmath last updated on 07/May/24

yes dear professor > 0

Commented by Frix last updated on 07/May/24

c > 0 \land s > 0 \Rightarrow \ln \frac{s}{c} = \ln s - \ln c

Commented by hardmath last updated on 07/May/24

Answer = 1 . ?

Commented by Frix last updated on 07/May/24

Yes for \cos x > 0 \land \sin x > 0 \land \cos x \neq \sin x

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