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सर्वसमिका `sec^(2)theta=1+tan^(2)theta` का प्रयोग करके सिद्ध कीजिए कि
`(sintheta-costheta+1)/(sinthea+costheta-1)=(1)/(sectheta-tantheta).`

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वाम पक्ष `=(sintheta-costheta+1)/(sintheta+costheta-1)=(costheta[tantheta-1+sectheta])/(costheta[tantheta+1-sectheta])`
`=(tantheta+sectheta-1)/(tantheta-sectheta+1)=((tantheta+sectheta)-1)/((tantheta-sectheta)+1)xx((tantheta-sectheta))/((tantheta-sectheta))`
`=((tan^(2)theta-sec^(2)theta)-(tantheta-sectheta))/([(tantheta-sectheta)+1](tantheta-sectheta))`
`=(-1-tantheta+sec theta)/((tantheta-sec theta+1)(tantheta-sectheta))`
`(-1(tantheta-sectheta+1))/(-1(tantheta-sectheta+1))`
`=(-1)/(tantheta-sectheta)=(1)/(sectheta-tantheta)=` दायाँ पक्ष।

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