Question

acosX+bsinX=m and asinX-bcosX=n then prove that a²+b²=m²+n² meritnation.com

Answer 1

Hi ,

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We know the trigonometric identity

Sin²A + cos² A = 1

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acos X + bsinX = m -----( 1 )

asinX - bcosX = n -------( 2 )

Do the square of equations ( 1 )

and ( 2) ,

And add resulting equations

a² cos² x+b² sin²x+2abcosxsinx +

a²sin² x + b² cos²x -2abcosxsinx

= m² + n²

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

( From above Trigonometric identity )

a² + b² = m² + n²

Hence proved .

I hope this helps you.

:)

Answer 2

Answer:

the above answer is correct