Sir please give me a detailed solution of this question as it is taken from RS Aggarwal book in which we have been asked to prove that (m²+n²)=(a²+b²) and we have given that acosθ+bsinθ = m and asinθ-bcosθ = n
Book – RS Aggarwal, Class 10, chapter 13B, question no 1
acosθ+bsinθ=m
Squaring equation, we get
a²cos²θ+b²sin²θ+2abcosθ=m²....(1)
Again square equation, asinθ−bcosθ=n
a²sin²θ+b²cos²θ−2abcosθsinθ=n²....(2)
Add (1) and (2)
a²cos²θ+b²sin²θ+2abcosθsinθ+a²sin²θ+b²cos²θ−2abcosθsinθ
=m²+n²
a²(cos²θ+sin²θ)+b²(cos²θ+sin²θ)=m²+n²
(Using cos²θ+sin²θ=1)
a²+b²=m²+n²
Hence proved.