Question

Solve the following questions. (Any one)
1 If a cos 0 + b sin 0 = m and a sin -b cos 0 = n, prove that a(square) + b(square) = m² + n (square)​

Answer 1

Question: If acosθ + bsinθ = m and asinθ - bcosθ = n. Prove that a² + b² = m² + n²

Solution:

ATQ,

acosθ + bsinθ = m

asinθ + bcosθ = n

LHS = m² + n²

= (acosθ + bsinθ)² + (asinθ - bcosθ)²

= a²cos²θ + b²sin²θ + 2acosθbsinθ + a²sin²θ + b²cos²θ - 2asinθbcosθ

= a²cos²θ + a²sin²θ + b²sin²θ + b²cos²θ + 2acosθbsinθ - 2asinθbcosθ

2acosθbsinθ - 2asinθbcosθ Gets cancelled.

= a²(cos²θ + sin²θ) + b²(sin²θ + cos²θ)

We know that sin²θ + cos²θ = 1

= a²(1) + b²(1)

= a² + b²

∴ a² + b² = m² + n²

LHS = RHS.

Hence Proved.

Answer 2

Answer:

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Refer to the attachment for solution ❤❤❤

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