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

Asked by suryap2 | 27th Sep, 2010, 08:14: AM

Expert Answer:

True.
(1 + cosA - sinA)2 = 2(1 + cosA)(1 - cosA)
(1 + 2(cosA - sinA) + (cosA - sinA)2 = 2(1 - cos2A)
(1 + 2(cosA - sinA) + (cos2A - 2sinAcosA + sin2A) = 2sin2A
1 + 2cosA - 2sinA + 1 - 2sinAcosA  = 2sin2A
2 + 2cosA - 2sinA - 2sinAcosA  = 2sin2A
1 + cosA - sinA - sinAcosA  = sin2A
Now if we put A = 45 we find LHS = RHS
Of course, we can put in the given expression directly any acute angle like 45, 60 or 30 and verify.
Regards,
Team,
TopperLearning.

Answered by  | 27th Sep, 2010, 08:44: AM

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