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What is Cos²A - Cos²B = ?

Answer 1

Carter Anderson

#=1/2(cos2A-cos2B)#

#cos^2A=1/2(1+cos2A)# #cos^2B=1/2(1+cos2B)#

Thus,

#cos^2A-cos^2B=1/2(1+cos2A)-1/2(1+cos2B)#

#=1/2(1+cos2A-1-cos2B)# #=1/2(cos2A-cos2B)#

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Answer 2

Anna Andrews

-sin(A+B)sin(A-B)

#cos^2A-cos^2B=(cosA+cosB)(cosA-cosB)#----------#color(red)(1)# Now,#cosA-cosB=2sin(A+B)//2 xx sin(B-A)//2# Or, #cosA-cosB=-2sin(A+B)//2 xx sin(A-B)//2#

Also,#cosA+cosB=2cos(A+B)//2xxcos(A-B)//2#

Plugging in the values in #color(red)(1)#,and rearranging,we get,

#{-2cos(A+B)//2xxsin(A+B)//2} xx {2sin(A-B)//2 xx cos(A-B)//2}# Thus,applying the formula #sin2x=2sinxcosx#,we have, #cos^2A-cos^2B=-sin(A+B)sin(A-B)#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.