maths
posted by Anonymous .
prove that the length of the perpendicular from the origin to the straight line joining the two points having coordinates ( a cos alpha, a sin alpha) and (a cos beta, a sin beta) is
a cos { ( alpha + beta)/2}.

both points are on a circle of radius a.
The distance to the line is the altitude of the triangle formed by the two points and the circle center.
Draw the diagram and see the answer checks.
Respond to this Question
Similar Questions

trig
express 20sin theta + 4 cos theta as R sin(theta + alpha) R sin(theta + alpha) = R cos(alpha)sin(theta) + R sin(alpha)cos(theta) > Rcos(alpha) = 20 Rsin(alpha) = 4 The xy coordinates of a point on a circle of radius R that … 
math
How would you establish this identity: (1+sec(beta))/(sec(beta))=(sin^2(beta))/(1cos(beta)) on the right, sin^2 = 1cos^2, that factor to 1cos * `1+cos, then the denominator makes the entire right side 1+cosB which is 1+1/sec which … 
verifying trigonometric identities
How do I do these problems? Verify the identity. a= alpha, b=beta, t= theta 1. (1 + sin a) (1  sin a)= cos^2a 2. cos^2b  sin^2b = 2cos^2b  1 3. sin^2a  sin^4a = cos^2a  cos^4a 4. (csc^2 t / cot t) = csc t sec t 5. (cot^2 t / csc 
Pre Calc.
Use the sum or difference identity to find the exact value of sin255 degrees. My answer: (sqrt(2) sqrt(6)) / (4) Find the value of tan (alphabeta), if cos alpha= 3/5, sin beta= 5/13, 90<alpha<180, and 90<beta<180. My … 
Math
how i solve this two equations ib order to find alpha and beta 2=cos(alpha)+1.341cos(beta) 2=sin(alpha)1.341sin(beta) 
Math
Given that sin alpha=4/sqrt65, pi/2<alpha<pi, and cos beta=3/sqrt13, tan beta>0, find the exact value of tan(alpha+beta) 
trig
evaluate the following in exact form, where the angeles alpha and beta satisfy the conditions: sin alpha=4/5 for pi/2 < alpha < pi tan beta=7/24 for pie < beta < 3pi/2 answer choices A. sin(beta+alpha) B. tan(betaalpha) … 
Math
using sin(alphabeta)=(sin alpha)(cos beta)(cos alpha)(sin beta) use the identity to derive the result proof for : sin(alphabeta) PLEASE PLEASE PLEASE HELP 
physics
A golfer takes two putts to sink the ball, one is (81.6 ft, 31.7 degrees N of E) and the other is (3.20 ft, 53.4 degrees W of N). What is the displacement of the single putt that would sink the ball on the first try? 
maths
if cos(alpha + beta)=0 then what will be the value of sin(alpha  beta)