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if sinA+sinB= root3(cos B-cos A) then sin3B+sin3A =

if sinA+sinB= root3(cos B-cos A) then sin3B+sin3A =

Grade:11

1 Answers

Askiitians_Expert Yagyadutt
askIITians Faculty 74 Points
10 years ago

Hello Hemanth ....

 

sinA + sinB = root(3) cosB - root(3)cosA

 

Divide by 2 both side

 

sinA / 2  + sinB / 2  = root(3).cosB/2 - root(3).cosA/2

 

1/2 . sinA  + root(3)/2 .cosA  =  root(3)/2 . cos(B)  - 1/2 . sin(B)

 

sin(A + 60)  = cos(B + 30)  =>  sin(A+60) = sin ( 60 - B )

 

so finaly  A + 60 = 60 - B

 

so A = -B

 

Therefore   Sin3B + sin3A  =  0  

 

I hope i have answered you :)

 

Regards

 

Yagya

askiitians_expert

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