What is Cos²A - Cos²B = ?

2 Answers
Shiva Prakash M V
Feb 16, 2018

#=1/2(cos2A-cos2B)#

Explanation:

#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)#

Shreya
Feb 16, 2018

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

Explanation:

#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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