If(x,y) be any point passing through (p/cosa,o) and (0,p/sina)then prove that xcosa+ysina=p

Question

If(x,y) be any point passing through (p/cosa,o) and (0,p/sina)then prove that xcosa+ysina=p

Answer 1

I assume you mean (x,y) is a point on the line passing through (p/cos a, 0) and (0, p/sin a). The slope of the line is

 

rise/run = (p/sin a - 0)/(0 - p/cos a) = (p/sin a)/(-p/cos a) = -cos a / sin a

 

By the slope-intercept form for a line,

 

y = -(cos a / sin a)(x - p/cos a)

 

Multiplying both sides by sin a, we get

 

y(sin a) = -(cos a)(x - p/cos a)

 

or

 

y(sin a) = -x(cos a) + p

 

Adding x(cos a) to both sides results in 

 

x(cos a) + y(sin a) = p

 

as desired.