Question

sec^6x-tan^6x=1+3 sec^2x tanc^2x

Answer 1

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