Prove : sec four A ( 1 - sin four A) - 2 tan square A = 1
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Step-by-step explanation:
sec⁴A(1-sin⁴A)-2tan²A
=sec⁴A-sec⁴Asin⁴A-2tan²A
=sec⁴A-sin⁴A(1/cos⁴A)-2tan²A
=sec⁴A-tan⁴A-2tan²A
={(sec²A)²-(tan²A)²}-2tan²A
=(sec²A+tan²A)(sec²A-tan²A)-2tan²A
=sec²A+tan²A-2tan²A [∵, sec²A-tan²A=1]
=sec²A-tan²A
=1
Hence proved
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