What is ln((sqrt(1+sin(x)))/(sqrt(1-sin(x)))) ?

The solution to ln((sqrt(1+sin(x)))/(sqrt(1-sin(x)))) is ln(sqrt(1+sin(x)))-ln(sqrt(1-sin(x)))

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simplify ln((sqrt(1+sin(x)))/(sqrt(1-sin(x))))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

ln ∣ y ∣ - ln ∣ y + 1 ∣

ln (\frac{x + 4}{x - 1})

2 lo g_{10} (x) + \frac{1}{2} lo g_{10} (x^{2} - 4)

ln (43.7575) + ln (0.7823) \cdot 55

(1 + 4 ln (3) - 9 ln (4)) - (- 1 + 4 ln (1) - 9 ln (2))

What is ln((sqrt(1+sin(x)))/(sqrt(1-sin(x)))) ?
The solution to ln((sqrt(1+sin(x)))/(sqrt(1-sin(x)))) is ln(sqrt(1+sin(x)))-ln(sqrt(1-sin(x)))