What is simplify-ln(cos(x))+ln(1+sin(x)) ?

The solution to simplify-ln(cos(x))+ln(1+sin(x)) is ln(sec(x)+tan(x))

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simplify-ln(cos(x))+ln(1+sin(x))

simplify

- ln (cos (x)) + ln (1 + sin (x))

ln (sec (x) + tan (x))

Solution steps

- ln (cos (x)) + ln (1 + sin (x))

Apply log rule:

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

ln (1 + sin (x)) - ln (cos (x)) = ln (\frac{sin ( x ) + 1}{cos ( x )})

= ln (\frac{1 + sin ( x )}{cos ( x )})

Simplify

\frac{1 + sin ( x )}{cos ( x )} : sec (x) + tan (x)

= ln (sec (x) + tan (x))

ln (a b^{n})

ln (1 - x) + ln (1 + x)

ln (\frac{2 y ^{2}}{z ^{3}})

- 0.3 \cdot lo g_{2} (0.3) - 0.7 \cdot lo g_{2} (0.7)

14.77 + 10 lo g_{10} (\frac{179.68}{1.905})

What is simplify-ln(cos(x))+ln(1+sin(x)) ?
The solution to simplify-ln(cos(x))+ln(1+sin(x)) is ln(sec(x)+tan(x))