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if sina=1/2 and sinb=1/3 then find the values of sin(a+b) and sin(2a+2b)

if sina=1/2 and sinb=1/3 then find the values of sin(a+b) and sin(2a+2b)
 

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Grade:10

1 Answers

harsh katara
13 Points
2 years ago
given, sin(a) =1/2 
          sin(b) = 1/3
we know sin2(\theta)+cos2(\theta) = 1
            cos(\theta) =[1-sin2(\theta)]1/2
                 therefore
           cos (a)=root 3 upon 2
          cos(b)=2root 2 upon 3
 
 now we also know \sin(a+b) = sina cosb + cosa sinb 
                                              = ½* 2root2/3 + root3/2 *1/3
                                              =2root2/6 +root3/6      ANS.
 now we also know sin(2\theta)= 2sin\thetacos\theta
                                sin[2(a+b)]= 2sin(a+b) cos(a+b)
                                                     2(2root2+root3)(36-2root2-root3)/36     ANS.

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