What is ln(1+tan(x/2))-ln(1-tan(x/2)) ?

The solution to ln(1+tan(x/2))-ln(1-tan(x/2)) is ln((1+tan(x/2))/(1-tan(x/2)))

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simplify ln(1+tan(x/2))-ln(1-tan(x/2))

simplify

ln (1 + tan (\frac{x}{2})) - ln (1 - tan (\frac{x}{2}))

ln (\frac{1 + tan ( \frac{x}{2} )}{1 - tan ( \frac{x}{2} )})

Solution steps

ln (1 + tan (\frac{x}{2})) - ln (1 - tan (\frac{x}{2}))

Apply log rule:

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

ln (1 + tan (\frac{x}{2})) - ln (1 - tan (\frac{x}{2})) = ln (\frac{tan ( \frac{x}{2} ) + 1}{- tan ( \frac{x}{2} ) + 1})

= ln (\frac{1 + tan ( \frac{x}{2} )}{1 - tan ( \frac{x}{2} )})

- lo g_{10} (1.36 \cdot 1 0^{- 5})

ln (5) + ln (7) - 3 ln^{2} (x)

lo g_{10} (\frac{x ^{2} y ^{5}}{z})

2 lo g_{b} (x) + 5 lo g_{b} (z)

lo g_{10} (10 x^{3} y)

What is ln(1+tan(x/2))-ln(1-tan(x/2)) ?
The solution to ln(1+tan(x/2))-ln(1-tan(x/2)) is ln((1+tan(x/2))/(1-tan(x/2)))