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यदि `sectheta+tantheta=p,` तो सिद्ध कीजिए कि `(p^(2)-1)/(p^(2)+1)=sintheta.`

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बायाँ पक्ष =`(p^(2)-1)/(p^(2)+1)`में `p=sec theta+tan theta` रखने पर,
`((sectheta+tantheta)^(2)-1)/((sectheta+tantheta)^(2)+1)=(sec^(2)theta+tan^(2)theta+2secthetatantheta-1)/(sec^(2)theta+tan^(2)theta+2secthetatantheta+1)`
`=(1+tan^(2)theta+tan^(2)theta+2secthetatantheta-1)/(sec^(2)theta+sec^(2)theta-1+2secthetatantheta+1)`
`=(2tan^(2)theta+2secthetatantheta)/(2sec^(2)theta+2sec thetatantheta)`
`=(2tantheta(tantheta+sectheta))/(2sectheta(sectheta+tantheta))=(tantheta)/(sectheta)`
`=(sintheta)/(costheta)xx(costheta)/(1)=sintheta=`दायाँ पक्ष।

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