Question

A cos a+ b sin a= m and a sin a- b cos a=n then a(square)+b(square)=? ​

Answer 1

Answer:

Given:-

a CosA + b SinA = m........(i)

a SinA - b CosA = n..........(ii)

Answer:-

m = a CosA + b SinA = m

Square both side in equation (i)

m² = (a CosA + b SinA)²

m² = a² Cos²A + b Sin²A + 2a CosA * b SinA...........(iii)

__________________________

n = a SinA - b CosA

Square both side in equation (ii)

n² = (a SinA - b CosA)²

n² = a² Cos²A + b² Sin²A - 2a CosA * b SinA..........(iv)

__________________________

Addequation (iii) and (iv)

m² + n² = a² Sin²A + b² Cos²A + a² Cos²A + b² Sin²A

[ 2a CosA * b SinA and - 2 CosA * b SinA are canceled while addition]

We know that Sin²A + Cos²A = 1

m² + n² = a² + b²

So,the value is a² + b²

Step-by-step explanation:

Answer 2

Answer:-

Explanation:-

Given:-

a CosA + b SinA = m........(i)

a SinA - b CosA = n..........(ii)

Answer:-

m = a CosA + b SinA = m

Square both side in equation (i)

m² = (a CosA + b SinA)²

m² = a² Cos²A + b Sin²A + 2a CosA * b SinA...........(iii)

__________________________

n = a SinA - b CosA

Square both side in equation (ii)

n² = (a SinA - b CosA)²

n² = a² Cos²A + b² Sin²A - 2a CosA * b SinA..........(iv)

__________________________

Addequation (iii) and (iv)

m² + n² = a² Sin²A + b² Cos²A + a² Cos²A + b² Sin²A

[ 2a CosA * b SinA and - 2 CosA * b SinA are canceled while addition]

We know that Sin²A + Cos²A = 1

m² + n² = a² + b²

So,the value is a² + b²