if tan A + sin A=m and tanA-sin A =n then proved that SecA=√mncosec^4 A
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mn= tan²A-sin²A
Rhs= ✓[(tan²A-sin²A)×cosec⁴A]
=✓[(tan²A-sin²A)×1/sin⁴A]
=✓[(1/cos²A-1)×1/sin²A]
=✓[(sec²A-1)×1/sin²A]
=✓[(tan²A)×1/sin²A]
=✓[sin²A/cos²A×1/sin²A]
=✓[1/cos²A]
=✓sec²A
=secA
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