已知为a锐角且sin(a—派⼀4)=√2⼀10求tan2a

2025-06-20 15:54:27
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回答1:

sin(a—π/4)=√2/10
又a∈(0,π/2),所以a-π/4∈(-π/4,π/4)
cos(a-π/4)=7√2/10
sin a=sin[(a-π/4)+π/4]=sin(a-π/4)cosπ/4+cos(a-π/4)sinπ/4=√2/10*√2/2+7√2/10*√2/2=4/5
cos a=3/5
tan a=4/3
tan2a=2tan a/1-tana
=-24/7