Trigonometeric Function

Help me friends.I am not able to solve it.

If tan( (pi/4) + y/2) = tan³ ( (pi/4) + x/2),

prove that sin(y)/ sin(x) = (3 + sin²x)/ (1+ 3sin²x)

2 Answers

1+tan(y/2)1-tan(y/2)=[1+tan(x/2)1-tan(x/2)]³

cos(y/2)+sin(y/2)cos(y/2)-sin(y/2)=[cos(x/2)+sin(x/2)cos(x/2)-sin(x/2)]³

1+siny1-siny=[1+sinx1-sinx]³

1+siny1-siny=1+3sinx+3sin²x+sin³x1-3sinx+3sin²x-sin³x

Applying componendo and dividendo...

siny=3sinx + sin³x1+3sin²x

sin ysin x=3 + sin²x1+3sin²x..(Hence proved)..:)

How far did you get?

Use the tangent addition identity and remember that tan(PI/4) = 1.

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