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paneg321
@paneg321
August 2022
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Вычислите 6cos(a/2) , если cosa=7/18 , 0<a<п/2
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Вычислите 6cos(a/2) , если cosa=7/18 , 0<a<п/2
cosa=cos²(a/2)-sin²(a/2)=2cos²(a/2)-1 ⇒cos²(a/2)=(cosa +1)/2
cos(a/2)=√[(cosa +1)/2]
6cos(a/2)=6·(√[(cosa +1)/2])= 6·(√[(7/18 +1)/2])=6·√(25/18)/2=3·5/(3√2)=5√2/2
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Verified answer
Вычислите 6cos(a/2) , если cosa=7/18 , 0<a<п/2cosa=cos²(a/2)-sin²(a/2)=2cos²(a/2)-1 ⇒cos²(a/2)=(cosa +1)/2
cos(a/2)=√[(cosa +1)/2]
6cos(a/2)=6·(√[(cosa +1)/2])= 6·(√[(7/18 +1)/2])=6·√(25/18)/2=3·5/(3√2)=5√2/2