Question

if x=a cos theta-b sin theta and y=a sin theta+b cos theta then probe that a^2+b^2=x^2+y^2​

Answer 1

Answer:

Step-by-step explanation:

first take the LHS

x²+y²=(acosФ-bsinФ)²+(asinФ+bcosФ)²

on expanding

acos²Ф+bsin²Ф-2acosФbsinФ+asin²Ф+bcos²Ф+2abcosФsinФ

on solving

a²(sin²Ф+cos²Ф)+b²(sin²Ф+cos²Ф)

since sin²Ф+cos²Ф=1 (trig identity)

a²+b² which is the RHS

hence proved that x²+y²=a²+b²