if the angle between two vectors is [b]a[/b] & [b]b[/b] is @ and angle between vectors [b]a[/b]+[b]b[/b] and [b]a[/b] is O
then
           [center]tan@=([b]b[/b]sinO )/([b]a[/b]+[b]b[/b]cosO )[/center]
now
[center]tan[sup]2[/sup] @=([b]b[/b]sinO)[sup]2[/sup]/([b]a[/b]+[b]b[/b]cosO)[sup]2[/sup] [/center]

now [center]tan[sup]2[/sup]@= sec[sup]2[/sup]@ -1
[/center]and [center]sec[sup]2[/sup]@ =1/cos[sup]2[/sup]@[/center]
[center]{[b]a[/b][sup]2[/sup] sec[sup]2[/sup]O + [b]b[/b][sup]2[/sup] + 2[b]a[/b][b]b[/b]secO}[/center]
so cos[sup]2[/sup]@=[center]____________________________________________________________________[/center]
[center]{[b]a[/b][sup]2[/sup]sec[sup]2[/sup]O + [b]b[/b][sup]2[/sup]sec[sup]2[/sup]O + 2[b]ab[/b]secO} [/center]


if @ =0
[center] [b]b[/b][sup]2[/sup]=[b]b[/b][sup]2[/sup]cos[sup]2[/sup]O[/center]
[center]O=0[/center]
if @ =90
[center][b]a[/b]=-[b]b[/b]cosO[/center]
if O=90
                          [center]-[b]b[/b][sup]2[/sup][/center]
tan[sup]2[/sup]@=[center] ____[/center]
[center][b]a[/b][sup]2[/sup]+[b]b[/b][sup]2[/sup][/center]




:) ;) :D ;D HERE BOLD CHARACTERS REPRESENT VECTORS.