求详解：已知α是锐角,且sin=(√6-√2)/4,则cosα=

sinα=(√6-√2)/4
cos^2α=1-[(√6-√2)/4]^2
cos^2α=1-(8-4√3)/16
cos^2α=(16-8+4√3)/16
cos^2α=(8+4√3)/16
cos^2α=(6+4√3+2)/16
cos^2α=[(√6+√2)/4]^2
cosα=±(√6+√2)/4
α是锐角cosα>0
所以cosα=(√6+√2)/4