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kartarkapoor2814:
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LHS = sec^6 A - tan^6 A
=> (sec²A)³ - (tan²A)³
=> (sec²A - tan²A) ( (sec²A)² + tan⁴A + sec²A tan²A)
=> we know that ,
sec²A = 1 + tan²A
=> sec²A - tan²A = 1
=> 1 [ ( 1+tan²A)² + tan⁴A + (1+tan²A) ( tan²A) ]
=> ( 1+tan²A )² + tan⁴A + tan²A + tan⁴A
=> 1 + tan⁴A + 2tan²A + tan⁴A + tan²A + tan⁴A
=> 1 + 3 tan⁴A + 3 tan²A
=> 1 + 3 tan²A + 3 tan⁴A
Since, LHS = RHS
=> Hence , Proved
=> (sec²A)³ - (tan²A)³
=> (sec²A - tan²A) ( (sec²A)² + tan⁴A + sec²A tan²A)
=> we know that ,
sec²A = 1 + tan²A
=> sec²A - tan²A = 1
=> 1 [ ( 1+tan²A)² + tan⁴A + (1+tan²A) ( tan²A) ]
=> ( 1+tan²A )² + tan⁴A + tan²A + tan⁴A
=> 1 + tan⁴A + 2tan²A + tan⁴A + tan²A + tan⁴A
=> 1 + 3 tan⁴A + 3 tan²A
=> 1 + 3 tan²A + 3 tan⁴A
Since, LHS = RHS
=> Hence , Proved
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