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已知cosa=√5/5,sin(a-b)=√10/10,且a,b是锐角,求cos(2a-b)
人气:399 ℃ 时间:2020-06-07 00:45:17
解答
cosb=cos(a+b-a)=cos(a+b)cosa+sim(a+b)sina.
=(-√10/10)(2√5/5+(3√10/10)(√5/5).
=√2/10.
sin(2a+b)=sin(a+b+a).
=sin(a+b)cosa+cos(a+b)sina.
=(3√10/10)(2√5/5)+(-√10/10)(√5/5).
=√2/2.
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