sec^6x-tan^6x=1+3tan^2+3tan^4x
aman26660th:
plz check question bro
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I think it is wrong question
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sec²x = 1 + tan²x
sec²x - tan²x = 1
LHS
= (sec²x)³ - (tan²x)³
= (sec²x - tan²x)(sec^4 x + sec²x tan²x + tan^4 x)
= 1*(sec^4 x - 2sec²xtan²x + tan^4 x + 3sec²xtan²x)
= (sec²x-tan²x)² + 3sec²xtan²x
= 1² + 3sec²xtan²x
= 1 + 3sec²xtan²x
= RHS
sec²x - tan²x = 1
LHS
= (sec²x)³ - (tan²x)³
= (sec²x - tan²x)(sec^4 x + sec²x tan²x + tan^4 x)
= 1*(sec^4 x - 2sec²xtan²x + tan^4 x + 3sec²xtan²x)
= (sec²x-tan²x)² + 3sec²xtan²x
= 1² + 3sec²xtan²x
= 1 + 3sec²xtan²x
= RHS
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