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Grade 11Trigonometry

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If tana,tanb are the roots of the equation x square + px + q = 0 (p is not equal to 0) then sin square (a+b) + psin(a+b) cos(a+b) + q cos square (a+b) =

Profile image of laxman
11 Years agoGrade 11
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1 Answer

Profile image of Y RAJYALAKSHMI
11 Years ago
Ans : q
 
 
since tana & tanb are roots of the equation, we have
sum of roots, tana + tanb = –p; product of roots tana * tanb = q
tan (a+b) = tana + tanb / 1 – tana tanb = -p/1-q
=> sin (a+b) = -p/root (p^2 +(1-q)^2)  &
cos (a+b) = 1-q/root (p^2 +(1-q)^2)
substituting these values we get sin^(a+b) + p sin(a+b) cos (a+b) + q cos^ (a+b) = q
 
 
 
 
 
 

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