This is an important question from the
Book- ML Aggarwal
Board- ICSE
Publication- Avichal
Chapter- Trigonometric Identities
Chapter number-18
If x = h + a cos θ and y = k + a sin θ, prove that (x – h)2 + (y – k)2 = a2.
Trigonometric Identities, class 10th, chapter 18th, question no 35, ICSE board, ML aggarwal..
We have been Given,
x = h + a cos θ
y = k + a sin θ
Now,
x – h = a cos θ
y – k = a sin θ
On squaring and adding we get
(x – h)2 + (y – k)2 = a2 cos2 θ + a2 sin2 θ
= a2 (sin2 θ + cos2 θ)
= a2 (1) [Since, sin2 θ + cos2 θ = 1]
– Hence proved