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If 3(siny – cosx) = 4(sinx + cosy), prove that sin3x / cos3y = 1

If 3(siny – cosx) = 4(sinx + cosy), prove that sin3x / cos3y = 1

Grade:12th pass

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:Hello student, please find answer to your question
3(siny - cosx) = 4(sinx + cosy)
\frac{sin3x}{cos3y} = 1
sin3x = cos3y
3sinx - 4sin^{3}x = 4cos^{3}y - 3cosy
3(sinx + cosy) = 4(cos^{3}y + sin^{3}y)
a^{3} + b^{3} = (a+b)(a^{2}-ab+b^{2})
cos^{3}y + sin^{3}x = (cosy+sinx)(cos^{2}y-cosy.sinx+sin^{2}x)
3(sinx + cosy) = 4 (cosy+sinx)(cos^{2}y-cosy.sinx+sin^{2}x)
3 = 4(cos^{2}y-cosy.sinx+sin^{2}x)
\Rightarrow 3(siny - cosx) = 4(sinx + cosy)
Y RAJYALAKSHMI
45 Points
9 years ago
Can you please explain how did you get the last step?

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