If `(sectheta+tantheta)(secphi+tanphi)(secPsi+tanPsi)=tanthetatanphitanPsi," then prove that "(sectheta-tantheta)(secphi-tanphi)(secPsi-tanPsi)=cotthe

Question

If `(sectheta+tantheta)(secphi+tanphi)(secPsi+tanPsi)=tanthetatanphitanPsi," then prove that "(sectheta-tantheta)(secphi-tanphi)(secPsi-tanPsi)=cotthe

If `(sectheta+tantheta)(secphi+tanphi)(secPsi+tanPsi)=tanthetatanphitanPsi," then prove that "(sectheta-tantheta)(secphi-tanphi)(secPsi-tanPsi)=cottheta.cotphi.cotPsi`

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Given `(sectheta+tantheta)(secphi+tanphi)(sec Psi+tanPsi)`
`=tanthetatanphitanPsi`
since`(sectheta-tantheta)=1/((sectheta+tantheta))`,we get
`(sectheta-tantheta)(secphi-tanphi)(secPsi-tanPsi)`
`=1/((sectheta+tantheta)(secphi+tanphi)(secPsi+tanPsi))`
`=1/(tanthetatanphitanPsi)=cottheta cotphicotPsi`

7 views Answered 2023-02-05 15:29