lets make the points ABCDE as shown below
DE∣∣BC(Given)
∠ACB=90° given∴∠AED=∠ACB=90°(as DE∣∣BC)∠ABC=∠ADE=α(corresponding angles as DE∣∣BC)∴in△ADE;∠AED=90°∴DE=ADcosα=xcosxDE=xcosαAE=ADsinα=xsinαAE=nsinαnow for△ADE and △ABC∠A is common∠AED=∠ACB=90°∴△ADE∽△ABC (byAA rule)∴ACAE=BCDE⟹xsinα+yxsinα=zxcosα⟹z=sinαcoaα(yxsinα)∴z=cotα(y+xsinα)z=ycotα+xcosα
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