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Two lines xcosalpha +ysinalpha =p1 and xcosbeta +ysinbeta =p2 are perpendicular to each other, then find the value of alpha + beta.

Asked by tarunkumardas32 2nd October 2020, 6:18 PM
Answered by Expert
Answer:
The two given lines are
straight x space cosα space plus space straight y space sinα space equals space straight p subscript 1 space
rightwards double arrow space straight y space equals space minus straight x space cosα over sinα plus straight p subscript 1 over sinα... space left parenthesis straight i right parenthesis
straight x space cosβ space plus thin space straight y space sinβ space equals space straight p subscript 2 space
rightwards double arrow space straight y space equals space minus straight x space cosβ over sinβ plus straight p subscript 1 over sinβ... space left parenthesis ii right parenthesis
As space the space lines space are space perpendicular comma space so space product space of space their space slopes space is space minus 1
rightwards double arrow space open parentheses negative cosα over sinα close parentheses open parentheses negative cosβ over sinβ close parentheses equals negative 1
rightwards double arrow space cos open parentheses straight alpha minus straight beta close parentheses equals 0
rightwards double arrow space straight alpha minus straight beta equals straight pi over 2
Answered by Expert 5th October 2020, 10:29 AM
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