PA28 INSTRUCTOR ALERTS STUDENT OF DEVELOPING CONFLICT AS COS LCL CTLR NEGLECTS TO ISSUE OTHER CONFLICTING CESSNA TFC ON BASE LEG TO ANOTHER RWY.

Narrative

I WAS RETURNING TO LAND AT COS FROM A CFI TRAINING FLT. I WAS FLYING FROM THE R SEAT AND MY INSTRUCTOR WAS IN THE L SEAT. AS WE APCHED COS; APCH CTL TOLD US TO 'EXPECT L BASE FOR RWY 17L.' WE WERE THEN HANDED OFF TO COS TWR ON 119.90. UPON RPTING IN TO COS TWR; WE WERE TOLD BY A CTLR TO ENTER L BASE FOR RWY 17L; THEN WERE TOLD TO CHANGE THAT TO RWY 12 AND THAT WE WERE CLRED TO LAND #2 FOLLOWING A CESSNA ON 1/2 MI FINAL FOR RWY 17R. WE RPTED BACK CLRED TO LAND #2 BEHIND THE CESSNA ON SHORT FINAL AND THAT WE HAD THE LNDG TFC IN SIGHT. WE WERE 2 MI OUT AND I WAS COMPLETING MY PRELNDG CHKS. AS I WAS TURNING BASE TO FINAL (SUN WAS A FACTOR); I WAS LOOKING DOWN TO RECONFIRM WE HAD 3 GREEN LIGHTS ON THE LNDG GEAR INDICATORS. AT THAT MOMENT; MY INSTRUCTOR YELLED 'WHOA' AND SHE IMMEDIATELY PUSHED FORWARD ON THE YOKE. I LOOKED UP AND SAW THE CESSNA HEADING TOWARD US AT A RANGE OF 1/2 MI AND BTWN 100-200 FT ABOVE. I; MYSELF; PUSHED FORWARD ON THE YOKE. AFTER THE CESSNA PASSED; ANOTHER CTLR CAME ON THE FREQ AND SAID 'SORRY ABOUT THAT CHEROKEE XXX; YOU ARE CLRED TO LAND ON RWY 12.' WE REPEATED CLRNC BACK TO HIM. HE REPEATED IT BACK TO US. I ONCE AGAIN REPEATED IT BACK. WE LANDED WITHOUT INCIDENT. I DON'T THINK THE OTHER CESSNA EVER SAW US. I BELIEVE HE WAS ON A DOWNWIND FOR RWY 17R. HE WAS INSTRUCTED TO LAND BEHIND US. IF HE WAS IN THE DOWNWIND FOR RWY 17R; THE TWR SHOULD HAVE HAD HIM DO A 360 DEG TURN FOR SPACING.