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| 1. |
If x=p sec theta +q tan theta and y= p tan theta + q sec theta than prove x2-y2=p2-q2 |
| Answer» x^2 - y^2 = (p sec theta + q tan theta)^2 - (p tan theta + q sec theta)^2= p^2 sec^2 theta + q^2 tan^2 theta + 2 pq sec theta tan theta - ( p^2 tan^2 theta + q^2 sec^2 theta + 2pq sec theta tan theta )= p^2 sec^2 theta + q^2 tan^2 theta + 2 pq sec theta tan theta - p^2 tan^2 theta - q^2 sec^2 theta - 2pq sec theta tan theta = p^2 sec^2 theta + q^2 tan^2 theta - p^2 tan^2 theta - q^2 sec^2 theta =p^2 (sec^2 theta - tan^2 theta) + q^2 (tan^2 theta - sec^2 theta)= p^2 (1) + q^2 (-1)= p^2 - q^2Hence proved | |