y=log1/2(sinx+cosx)+log1/2(cosx-sinx)单调区间

y=log1/2(sinx+cosx)+log1/2(cosx-sinx)单调区间
y=log1/2(sinx+cosx)+log1/2(cosx-sinx)单调区间

y=log1/2(sinx+cosx)+log1/2(cosx-sinx)单调区间
y=log1/2(sinx+cosx)+log1/2(cosx-sinx)
=log1/2 (sinx+cosx)(cosx-sinx)
=log1/2 (cos²x-sin²x)
=log1/2 cos2x
由于log1/2 x为递减函数,
所以y=log1/2 cos2x的单调性和cos2x＞0的单调性相反,
cos2x满足cos2x＞0的单调减区间为2x∈[2kπ,π/2+2kπ],
即x∈[kπ,π/4+kπ],
cos2x满足cos2x＞0的单调增区间为2x∈[-π/2+2kπ,2kπ],
即x∈[-π/4+kπ,kπ],
即y=log1/2(sinx+cosx)+log1/2(cosx-sinx)
单调增区间为[kπ,π/4+kπ],减区间为[-π/4+kπ,kπ].