how to prove that cosA^4-sina^4=cosA^2-sinA^2 is an identity

Asked by  | 26th Aug, 2009, 05:38: PM

Expert Answer:

LHS =

(cos A)4 - (sin A)4

= [(cos A)2 - (sin A)2 ][(cos A)2 + (sin A)2 ] ..............................{ a2 - b2 = (a+b)(a-b) }

= (cos A)2 - (sin A)2      .............................    { [(cos A)2 + (sin A)2 ] = cos2A + sin2A = 1} 

Regards,

Team,

TopperLearning.

Answered by  | 26th Aug, 2009, 09:02: PM

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