which of the following are true?

Asked by suryap2 | 9th Aug, 2010, 09:56: PM

Expert Answer:

cos4A - cos2A = LHS
cos2A(cos2A - 1) = (1 - sin2A)(-sin2A) = sin4A - sin2A = RHS 
First identity is true.
sin6A + cos6A  = 1 - 3sin2Acos2A
sin6A + cos6A  + 3sin2Acos2A = 1
 sin6A + cos6A  + 3sin2Acos2A(sin2A + cos2A) = 1
(sin2A + cos2A)3 = 1
1 = 1
Second identity is also true.
sec4A + sec2A = tan4A + tan2A
sec4A + sec2A = tan2A(tan2A + 1)
 
sec4A + sec2A = tan2A(sec2A)
sec4A + sec2A = (sec2A - 1)(sec2A)
sec4A + sec2A = sec4A - sec2A
Third identity is not true.
cot4A - 1 = cosec4A - 2cosec2A
cot4A - 1 = cosec2A(cosec2A - 2)
 cot4A - 1 = (1 + cot2A)(cot2A - 1)
 cot4A - 1 =  cot4A - 1
This identity is also true.
 
Regards,
Team,
TopperLearning.

Answered by  | 28th Sep, 2010, 03:16: PM

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