Question

Verify the identity. (Simplify at each step.) cos(x + y)cos(x - y) = cos^2(x) - sin^2(y) cos(x + y)cos(x - y) = (cos(x)cos(y) - ( ))(( ) + sin(x)sin(y)) = cos^2(x)cos^2(y) - sin^2(x)( ) = cos^2(x)(1 - ) - sin^2(x)( ) = cos^2(x) - cos^2(x)( ) - sin^2(x)( ) = cos^2(x) - ( )(cos^2(x) + sin^2(x)) = cos^2(x) - sin^2(y)

          Verify the identity. (Simplify at each step.)
cos(x + y)cos(x - y) = cos^2(x) - sin^2(y)
cos(x + y)cos(x - y) = (cos(x)cos(y) - ( ))(( ) + sin(x)sin(y))
= cos^2(x)cos^2(y) - sin^2(x)( )
= cos^2(x)(1 - ) - sin^2(x)( )
= cos^2(x) - cos^2(x)( ) - sin^2(x)( )
= cos^2(x) - ( )(cos^2(x) + sin^2(x))
= cos^2(x) - sin^2(y)

Verify the identity. (Simplify at each step.)
cos(x + y)cos(x - y) = cos^2(x) - sin^2(y)
cos(x + y)cos(x - y) = (cos(x)cos(y) - ( ))(( ) + sin(x)sin(y))
= cos^2(x)cos^2(y) - sin^2(x)( )
= cos^2(x)(1 - ) - sin^2(x)( )
= cos^2(x) - cos^2(x)( ) - sin^2(x)( )
= cos^2(x) - ( )(cos^2(x) + sin^2(x))
= cos^2(x) - sin^2(y)

Added by Jennifer W.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Suman Saurav Thakur

03/28/2022

Step 1

Step 1: Using the cosine addition formula, we have: \[ \cos(x - y)\cos(x + y) = (\cos x \cos y + \sin x \sin y)(\cos x \cos y - \sin x \sin y) \] Show more…

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Verify the identity. (Simplify at each step) cos(x - y)cos(x + y) = cos^2(x) - sin^2(y) cos(x - y)cos(x + y) cos(x)cos(y) sin(x)sin(y) cos^2(x) - sin^2(y) cos^2(x) - sin^2(x) cos^2(x) - (1 - cos^2(x)) 2cos^2(x) - 1