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Cos x = 3/√10

log(sinx) + log(cosx) + log(tanx)

= log(sinx × cosx × tanx ) [using log (a) +log (b) = log (ab)]

= log ( sinx × cosx ×(sinx/cosx))

=log (sinx × sinx)

=log (sin²x)

sin²x = 1 - cos²x = 1 - (3/√10)² = 1 - (9/10) = (10-9)/10 = 1/10

log(sin²x) = log(1/10) =

log(sinx) + log(cosx) + log(tanx)

= log(sinx × cosx × tanx ) [using log (a) +log (b) = log (ab)]

= log ( sinx × cosx ×(sinx/cosx))

=log (sinx × sinx)

=log (sin²x)

sin²x = 1 - cos²x = 1 - (3/√10)² = 1 - (9/10) = (10-9)/10 = 1/10

log(sin²x) = log(1/10) =

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