Question 873143
if sin alpha =2/3 for pi/2≤alpha≤pi and cos beta =-5/7 for pi≤beta≤3pi/2, find the value of cos(alpha+beta)
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{{{sin(alpha)=2/3}}} (in quadrant II in which sin>0, cos<0)
{{{cos(alpha)=-sqrt(1-sin^2(alpha))=-sqrt(1-(4/9))=-sqrt(5/9)=-sqrt(5)/3)}}}
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{{{cos(beta)=-5/7}}} (in quadrant III in which sin<0, cos<0)
{{{sin(beta)=-sqrt(1-cos^2(beta))=-sqrt(1-(25/49))=-sqrt(24/49)=-sqrt(24)/7)}}}
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{{{cos(alpha)+(beta)=cos(alpha)*cos(beta)-sin(alpha)*sin(beta)}}}
{{{cos(alpha)+(beta)=-(sqrt(5)/3)*(-5/7)-(2/3)*(-sqrt(24)/7)=5sqrt(5)/21+2sqrt(24)/21=(5sqrt(5)+2sqrt(24))/21}}}