Sec^6x - tan^6x - 3 Sec²x.tan²x = 1
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Answer:
LHS=sec⁶x-tan⁶x-3sec²x.tan²x
=(sec²x)³-(tan²x)³-3sec²x.tan²x
=(sec²x-tan²x)(sec⁴x+sec²x.tan²x+tan⁴x) - 3sec²x.tan²x
=sec⁴x+tan⁴x+sec²x.tan²x-3sec²x.tan²x
=sec⁴x-2sec²x.tan²x+tan⁴x
=(sec²x-tan²x)²
=1²
=1=RHS
HENCE PROVED
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