化简-ln(cos(x))+ln(cos(y))

解答

化简

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

ln (sec (x) cos (y))

求解步骤

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

使用对数计算法则:

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 )})

使用基本三角恒等式:

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

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

s im pl i f y \frac{1}{2} (ln (x) - ln (y)) + 3 ln (z)

s im pl i f y ln (\frac{1}{x ^{y}})

s im pl i f y ln ((a + 1) x^{a})

s im pl i f y - ln (\frac{2}{3}) - \frac{1}{3}

s im pl i f y ln (- 6 \cdot \frac{e ^{2.39209}}{3})