prove the identity:sec^6o=tan^6+3tan^2o.sec^2o+1
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Recall that 1 + tan2x = sec2x and A3-B3 = (A-B)(A2+AB+B2)
Solution:-
sec6x - tan6x = (sec2x)3 - (tan2x)3
= (sec2x - tan2x)(sec4x + sec2xtan2x + tan4x)
= (1+tan2x-tan2x))[sec4x+sec2xtan2x+(sec2x-1)tan2x]
= sec4x - tan2x + 2sec2xtan2x
= sec2x(1+tan2x) - tan2x + 2sec2xtan2x
= sec2x - tan2x + sec2xtan2x + 2sec2xtan2x
= 1 + 3sec2xtan2x
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Solution:-
sec6x - tan6x = (sec2x)3 - (tan2x)3
= (sec2x - tan2x)(sec4x + sec2xtan2x + tan4x)
= (1+tan2x-tan2x))[sec4x+sec2xtan2x+(sec2x-1)tan2x]
= sec4x - tan2x + 2sec2xtan2x
= sec2x(1+tan2x) - tan2x + 2sec2xtan2x
= sec2x - tan2x + sec2xtan2x + 2sec2xtan2x
= 1 + 3sec2xtan2x
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vinayaka777:
tnk u
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