Question

If a cos x + b sin x = m and a sin x – b cos x = n, prove that a^2 + b^2 = m^2 + n^2

Answer 1

Hi ,

a cosx + b sinx = m ---( 1 )

a sinx - b cos x = n ---( 2 )

do the Square of both the equations and

add them ,

( a²cos² x + b²sin² x + 2abcosxsinx )+ ( a² sin² x

+ b²cos² x - 2abcosxsinx ) = m² + n²

a²(cos² x + sin² x ) + b²(sin² x+cos² x ) = m²+n²

a² + b² = m² + n²

[ since cos² x + sin² x = 1 ]

Hence proved.

I hope this helps you.

: )

Answer 2

Step-by-step explanation:

Hello

I hope it helps you:)

Answer is in the attachment below:-