Question

prove that
$\sf cos (A+B)×cos (A-B)=cos^2A-sin^2B$


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Answer 1

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

=> (cosA cosB - sinA sinB) (cosA cosB+ sinA sinB)

=> cos²A cos²B - sin²A sin²B

=> cosA (1-sin²B) - (1 - cos²A) sin²B + cos²A sin²B

=> cos²A - sin²B

$\huge \mathtt \purple{@VioletMoon}$

Answer 2

$\huge\boxed{\fcolorbox{white}{pink}{AnsweR}}$

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

=> (cosA cosB - sinA sinB) (cosA cosB+ sinA sinB)

=> cos²A cos²B - sin²A sin²B

=> cosA (1-sin²B) - (1 - cos²A) sin²B + cos²A sin²B

=> cos²A - sin²B

$\huge\purple{\mathfrak{@ʂɧı۷ą4548}}$