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If (sectheta+tantheta)(secphi+tanphi)(se...

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

Text Solution

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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`
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