f(x)=lg(sinx+根号1+sin²x)的奇偶性?f(-x) =lg[-sinx+√(1+sin²x)] =lg{[-sin²+(1+sin²x)]/[sinx+√(1+sin²)]}没看懂,

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f(x)=lg(sinx+根号1+sin²x)的奇偶性?f(-x) =lg[-sinx+√(1+sin²x)] =lg{[-sin²+(1+sin²x)]/[sinx+√(1+sin²)]}没看懂,
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f(x)=lg(sinx+根号1+sin²x)的奇偶性?f(-x) =lg[-sinx+√(1+sin²x)] =lg{[-sin²+(1+sin²x)]/[sinx+√(1+sin²)]}没看懂,
f(x)=lg(sinx+根号1+sin²x)的奇偶性?
f(-x) =lg[-sinx+√(1+sin²x)] =lg{[-sin²+(1+sin²x)]/[sinx+√(1+sin²)]}
没看懂,

f(x)=lg(sinx+根号1+sin²x)的奇偶性?f(-x) =lg[-sinx+√(1+sin²x)] =lg{[-sin²+(1+sin²x)]/[sinx+√(1+sin²)]}没看懂,
√(1+sin²x)-sinx=[√(1+sin²x)-sinx] * [√(1+sin²x)+sinx] / [√(1+sin²x)+sinx]
=[(1+sin²x)-sin²]/[√(1+sin²)+sinx]
=1/[√(1+sin²)+sinx]

f(-x)=lg(sin(-x)+根号1+sin²(-x))
=lg(-sinx+根号1+sin²x)
真数分子分母同乘(sinx+√(1+sin²x))
=lg{[-sin²x+(1+sin²x)]/[sinx+√(1+sin²)]}
=lg1/(sinx+√(1+sin²))
=-lg(sinx+√(1+sin²))
=-f(x)