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`(1+ tan theta + sec theta) ( 1+ cot theta - cosec theta)` बराबर है :

Answer

c

Explanation

`(1 + tan theta + sec theta) ( 1 + cot thea - cosec theta)`
` = 1+ cot theta - cosec theta + tan theta + tan theta * cot theta `
`-tan theta * cosec theta +sec theta + sec theta * cot theta - sec theta * cosec theta `
`= 1 + cot theta - cosec theta + tan theta`
`+(sin theta)/(cos theta) * (cos theta)/( sin theta) - (sin theta)/(cos theta) * (1)/( sin theta) + sec theta`
`+ (1)/(cos theta) * (cos theta)/(sin theta) - sec theta cosec theta `
`= 1 + ( cot theta + tan theta) - cosec theta)`
`+ 1 - sec theta + sec theta + cosec theta`
`- sec theta cosec theta`
` = 2 + ((cos theta)/(sin theta)+ (sin theta)/(cos theta))-sec theta cosec theta `
`= 2 + (cos^(2) theta + sin^(2) theta)/(sin theta * cos theta) - sec theta cosec theta`