> 1 = cos(theta)  *r2/r1
> 
> Therefore: cos(theta)  = r2/r1

You messed up at the very last step :-)

Easier if at this step:

sin(theta)/cos(theta)  = sin(theta)  * r2/r1

You just cancel the sin(theta) term on each side, leaves you with:

1/cos(theta) = r2/r1

Taking the reciprocal of both sides then leaves you with the answer.

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