Question

eliminate theta if a cos theta + b sin theta equals to M and a sin theta minus B cos theta equals to n​

Answer 1

Theta is written as A.

Answer:

a^2 + b^2 = m^2 + n^2.

Step-by-step explanation:

Given,

      ⇒ acosA + bsinA = m     ...( 1 )

      ⇒ asinA - bcosA = n       ...( 2 )

Squaring on both sides of ( 1 ) :

⇒ ( acosA + bsinA )^2 = m^2

⇒ a^2 cos^2 A + b^2 sin^2 A + 2absinAcosA = m^2    ..( 3 )

Squaring on both sides of ( 2 ):

⇒ ( asinA - bcosA )^2 = n^2

⇒ a^2 sin^2 A + b cos^2 A - 2absinAcosA = n^2        ...( 4 )

Adding ( 3 ) and ( 4 ) :

⇒ ( a^2 cos^2 A + b^2 sin^2 A + 2absinAcosA ) + ( a^2 sin^2 A + b cos^2 A - 2absinAcosA ) = m^2 + n^2

⇒ a^2( cos^2 A + sin^2 A ) + b^2( sin^2 A + cos^2 A ) = m^2 + n^2

⇒ a^2 + b^2 = m^2 + n^2         { sin^2 A + cos^2 A = 1 }