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ML Aggarwal Solutions Class 10 Mathematics Solutions for Trigonometric Identities Exercise 18 in Chapter 18 - Trigonometric Identities
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If x = h + a cos θ and y = k + a sin θ, prove that (x – h)2 + (y – k)2 = a2.
Answer:
Solution:
Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence.
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
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