Question

sinA+sinB=√3(cosB-cosA) thensin3A+sin3B=?

Options 1)0

2)2

3)1

4) -1

Answer 1

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if sinA+sinB= root3(cos B-cos A) then sin3B+sin3A =
7 years ago
Answers : (1)
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