Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 years ago

Cos(A+B)cos(A-B) = cos^2 -sin^2B please show the workings in all areas for best answer?

Update:

Sorry. It is supposed to equal cos^2A - sin^2B

3 Answers

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  • 2 years ago
    Favorite Answer

    LHS = cos(A+B) cos( A-B)

    =(cosAcosB - sinAsinB)(cosAcosB + sinAsinB)

    = (cosA cosB)² - (sinA sinB)²

    = cos²A cos²B - sin²A sin²B

    =cos²A ( 1-sin²B) - (1 - cos²A) sin²B

    =( cos ²A - cos²A sin ²B) - (sin²B - cos²A sin²B)

    = cos² A - sin²B = RHS .......proved

    Source(s): Note : • cos(A+B) = (cosAcosB - sinAsinB) • cos(A-B) = (cosAcosB + sinAsinB) • (x - y)(x + y) = x² - y² • cos²B = 1 - sin²B • sin²A = 1 - cos²A
  • ted s
    Lv 7
    2 years ago

    comment : won't equal what you typed !!....uses the concept of ( x - y ) ( x + y ) = x² - y² where x = cos A cos B and y = sin A sin B.... as well as cos² Θ + sin² Θ = 1 ....try it

  • Anonymous
    2 years ago

    Answer is 20

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