Question

If a cos theta + b sin theta = 4 and a sin theta -b cos theta = 3, then
a^2+ b^2 is equal to​

Answer 1

Answer:

a²+b² = 25

Step-by-step explanation:

Given: acosβ+bsinβ = 4 ---------1

Also, asinβ-bcosβ = 3 ---------2

On squaring and adding equation 1 and 2, we get

(acosβ+bsinβ)²+(asinβ-bcosβ)² = 4²+3²

a²cos²β + b²sin²β + 2absinβcosβ + a²sin²β + b²cos²β - 2absinβcosβ = 16+9

or a²cos²β + a²sin²β + b²sin²β + b²cos²β = 25

or a²(cos²β + sin²β) + b²(sin²β + cos²β) = 25

or a²+b² = 25

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