prove that (cosa-cosb)²+(sina-sinb)²=4 sin²(a-b/2)
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L.H.S,= { cosA - cosB }^2 + {sinA -sinB}^2
[sinC-sinD= 2cosC+D)/2 sin(C-D)/2&cosC-cosD=2sin(C+D)/2sin(D-C)...
= { 2 sin(A+B)/2 sin(B- A)/2}^2 + { 2cos(A+B)/2 sin(A-B)/2}^2
=4 sin^2(A-B)/2 [ sin^2(A+B)/2 + cos^2(A+B)/2 ]
= 4 sin^2(A- B)/2 *1
= R.H.S.
Step-by-step explanation:
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