Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Miscellaneous

Misc 1
Important

Misc 2 Important

Misc 3

Misc 4 You are here

Misc 5 Important

Misc 6

Misc 7 Important

Misc 8 Important

Misc 9

Misc 10 Important

Misc 11 Important

Misc 12

Misc 13

Misc 14 Important

Misc 15 Important

Misc 16

Misc 17 Important

Misc 18 Important

Misc 19 Important

Misc 20 Important

Misc 21 Important

Misc 22

Misc 23 Important

Question 1 Important Deleted for CBSE Board 2024 Exams

Last updated at May 29, 2023 by Teachoo

Misc 4 Find the perpendicular distance from the origin to the line joining the points (cos , sin ) and (cos , sin ) . Frist we find equation of line We know that equation of line joining two point (x1, y1) & (x2, y2) is (y y1) = ( 2 1)/( 2 1) (x x1) Equation of line passing through (cos , sin ) & (cos , sin ) is (y sin ) = (sin sin )/(cos cos ) (x cos ) (cos cos ) (y sin ) = ("sin " " " " sin " )(x cos ) cos (y sin ) cos (y sin ) = "sin " (x cos ) sin (x cos ) cos y cos sin cos y + cos sin = sin x sin cos sin x + sin cos cos y cos sin cos y + cos sin = sin x sin cos sin x + sin cos cos y cos y cos sin + cos sin = sin x sin x sin cos + sin cos (cos cos )y cos sin + cos sin = (sin sin )x sin cos + sin cos (cos cos )y (sin sin )x = "sin " " cos "+" sin cos "+ " cos " " sin " "cos sin " (cos cos )y (sin sin )x = sin cos + cos sin (sin sin )x + (cos cos )y = sin cos + cos sin (sin sin )x + (cos cos )y = cos sin sin cos (sin sin )x + (cos - cos )y = sin cos sin cos (sin sin )x + (cos - cos )y = sin ( ) (sin sin )x + (cos - cos )y sin ( ) = 0 The above equation is of the form Ax + By + C = 0 Here A = (sin sin ) , B = (cos cos ) , C = sin ( ) We know that distance of a point (x1, y1) from line Ax + By + C = 0 is d = | _1 + _1 + |/ ( ^2 + ^2 ) Distance of origin (0, 0) to the line (sin sin )x + (cos - cos )y = sin ( ) is d = | _1 + _1 + |/ ( ^2 + ^2 ) Putting values d = | "(" sin " " sin ")" 0 + "(" cos " " " " cos ")" 0 + ( sin ( )|/ ( "(" sin " " sin ")" ^2 + "(" cos " " " " cos ")" ^2 ) d = |0 + 0 sin ( )|/ ( "(" sin " " sin ")" ^2 + "(" cos " " " " cos ")" ^2 ) d = | sin ( )|/ ( "(" sin " " sin ")" ^2 + "(" cos " " " " cos ")" ^2 ) d = | sin ( + )|/ ( "(" sin " " sin ")" ^2 + "(" cos " " " " cos ")" ^2 ) d = | sin ( )|/ ( "(" sin " " sin ")" ^2 + "(" cos " " " " cos ")" ^2 ) d = | sin ( )|/ ((2cos (( " " + " " )/2)". " sin (( " " )/2))^2+( 2 sin (( " " + " " )/2)"." sin(( " " )/2))^2 ) d = | sin ( )|/ (4cos^2 (( " " + " " )/2)"." sin^2 (( " " )/2)+ " " 4 sin ^2 (( " " + " " )/2)"." sin^2 (( " " )/2) ) d = | sin ( )|/ (4 sin ^2 (( " " )/2)(cos^2 (( " " + " " )/2)+ sin ^2 (( " " + " " )/2)) ) d = | sin ( )|/( (4 sin ^2 (( " " )/2).1) ) d = | sin ( )|/ (2^2 ^2 (( " " )/2) ) d = | sin ( )|/(2 | (( " " )/2)| ) Thus, the required distance is | sin ( )|/(2 | (( " " )/2)| )