prove true or false: (1+cosA-sinA)^2 = 2(1+cosA).(1-sinA)

Asked by suryap2 | 27th Sep, 2010, 08:08: AM

Expert Answer:

True.
 
LHS = [1 + (cosA - sinA)]2
=1+(cosA-sinA)2+2(cosA-sinA)
=1+cos2A+sin2A-2sinAcosA+2cosA-2sinA
=1+1-2sinAcosA+2cosA-2sinA
=2-2sinA-2sinAcosA+2cosA
=2(1-sinA)+2cosA(1-sinA)
=2(1-sinA)(1+cosA)
 
LHS = RHS
 
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Team,
TopperLearning.

Answered by  | 28th Sep, 2010, 04:37: PM

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