What is simplify-ln(cos(x))+ln(cos(y)) ?

The solution to simplify-ln(cos(x))+ln(cos(y)) is ln(sec(x)cos(y))

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simplify-ln(cos(x))+ln(cos(y))

simplify

- ln (cos (x)) + ln (cos (y))

ln (sec (x) cos (y))

Solution steps

- ln (cos (x)) + ln (cos (y))

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (cos (y)) - ln (cos (x)) = ln (\frac{cos ( y )}{cos ( x )})

= ln (\frac{cos ( y )}{cos ( x )})

Use the basic trigonometric identity:

\frac{1}{cos ( x )} = sec (x)

= ln (sec (x) cos (y))

\frac{1}{3} ln (16 p) - 3 ln (2 pq) - 2 ln (5 p^{4}) + 6 ln (q)

ln (17) - 2 ln (x) + 3 ln (y)

\frac{1}{2} (ln (x) - ln (y)) + 3 ln (z)

ln (\frac{15}{22})

ln (\frac{7}{6}) - ln (\frac{5}{6})

What is simplify-ln(cos(x))+ln(cos(y)) ?
The solution to simplify-ln(cos(x))+ln(cos(y)) is ln(sec(x)cos(y))