If $$($$$$sec$$⁡A−$$tan$$⁡$$A)($$$$sec$$⁡B−$$tan$$⁡$$B)($$$$sec$$⁡C−$$tan$$⁡$$C)$$ $$=($$$$sec$$⁡$$A+$$$$tan$$⁡$$A)($$$$sec$$⁡$$B+$$$$tan$$⁡$$B)($$$$sec$$⁡$$C+$$$$tan$$⁡$$C)$$ then each side is equal to

Question

If $$($$$$sec$$⁡A−$$tan$$⁡$$A)($$$$sec$$⁡B−$$tan$$⁡$$B)($$$$sec$$⁡C−$$tan$$⁡$$C)$$ $$=($$$$sec$$⁡$$A+$$$$tan$$⁡$$A)($$$$sec$$⁡$$B+$$$$tan$$⁡$$B)($$$$sec$$⁡$$C+$$$$tan$$⁡$$C)$$ then each side is equal to

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We have,$$($$$$sec$$⁡A−$$tan$$⁡$$A)($$$$sec$$⁡B−$$tan$$⁡$$B)($$$$sec$$⁡C−$$tan$$⁡$$C)=($$$$sec$$⁡$$A+$$$$tan$$⁡$$A)($$$$sec$$⁡$$B+$$$$tan$$⁡$$B)($$$$sec$$⁡$$C+$$$$tan$$⁡$$C)$$⇒$$sec2$$⁡A−$$tan2$$⁡$$Asec2$$⁡B−$$tan2$$⁡$$Bsec2$$⁡C−$$tan2$$⁡$$C={($$$$sec$$⁡$$A+$$$$tan$$⁡$$A)($$$$sec$$⁡$$B+$$$$tan$$⁡$$B)(scc$$⁡$$C+$$$$tan$$⁡$$C)}2$$⇒$$1={($$$$sec$$⁡$$A+$$$$tan$$⁡$$A)($$$$sec$$⁡$$B+$$$$tan$$⁡$$B)($$$$sec$$⁡$$C+$$$$tan$$⁡$$C)}2$$⇒$$($$$$sec$$⁡$$A+$$$$tan$$⁡$$A)($$$$sec$$⁡$$B+$$$$tan$$⁡$$B)($$$$sec$$⁡$$C+$$$$tan$$⁡$$C)=$$±$$1Hence$$, $$LHS=RHS=$$±$$1$$.

If $(\sec A - \tan A) (\sec B - \tan B) (\sec C - \tan C)$ $= (\sec A + \tan A) (\sec B + \tan B) (\sec C + \tan C)$ then each side is equal to

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If (sec⁡A−tan⁡A)(sec⁡B−tan⁡B)(sec⁡C−tan⁡C) =(sec⁡A+tan⁡A)(sec⁡B+tan⁡B)(sec⁡C+tan⁡C) then each side is equal to

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If $(\sec A - \tan A) (\sec B - \tan B) (\sec C - \tan C)$ $= (\sec A + \tan A) (\sec B + \tan B) (\sec C + \tan C)$ then each side is equal to