Question

calculați cos(a+b) și sin(a-b),știind că a,b € (0,p/2), sinA=7/25 si sinB=12/13

Answer 1

a,b € (0,p/2) ==> sin,cos +

$sin^x+cos^x=1$

$cos^2A=1-sin^2A \ =1- \frac{49}{625}=\frac{625-49}{625} =\frac{576}{625}$

$cosA=\sqrt{\frac{576}{625}} =\frac{24}{25}$

$cos^2B=1-sin^2B \ =1- \frac{144}{169}=\frac{169-144}{169} =\frac{25}{169}$

$cosB=\sqrt{\frac{25}{169}} =\frac{5}{13}$

$cos(a+b)=cosa*cosb-sina*sinb= \frac{5}{13} *\frac{24}{25} -\frac{7}{25}*\frac{12}{13} = \frac{120-84}{325} =\frac{36}{325}$

$sin(a-b)=sina*cosb-sinb*cosa=\frac{7}{25} *\frac{5}{13} -\frac{12}{13}*\frac{24}{25 } = \frac{35-288}{325} =\frac{-253}{325}$