f(x)=㏑|secx+tanx|= f(x)
= ㏑|1/cosx+sinx/cosx|
= ㏑|(1+sinx)/cosx|
= ln|[sin(x/2)+cos(x/2)]²/[(cos²(x/2)-sin²(x/2)] |
= ln |[sin(x/2)+cos(x/2)]/[cos(x/2)-sin(x/2)] |
= ln |[1+tan(x/2)]/[1-tan(x/2)] |
f(-x) = ln |[1+tan(-x/2)]/[1-tan(-x/2)] |
= ln |[1-tan(x/2)]/[1+tan(x/2)] |
f(x)+f(-x) = ln |[1+tan(x/2)]/[1-tan(x/2)] | + ln |[1-tan(x/2)]/[1+tan(x/2)] |
= ln |[1+tan(x/2)]/[1-tan(x/2)] * [1-tan(x/2)]/[1+tan(x/2)] |
= ln1 = 0
∴ 奇函数
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