The value of (1 + cot $\theta$ − cosec $\theta$) (1 + tan $\theta$ + sec $\theta$) is

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KollegeApply · Accepted Answer

The given expression is `(1+cot $\theta$-cosec $\theta$ )(1+tan $\theta$+sec $\theta$)` Simplifying the given expression, we have `(1+cot $\theta$-cosec $\theta$)(1+tan $\theta$+sec $\theta$) =(1+cos $\theta$/sin $\theta$-1/sin $\theta$)(1+sin $\theta$/cos $\theta$+1/cos $\theta$) = (sin $\theta$+cos $\theta$-1)/sin $\theta$xx (cos $\theta$+sin $\theta$+1)/cos $\theta$ = ((sin $\theta$+cos $\theta$-1)(cos $\theta$+sin $\theta$+1))/(sin $\theta$cos $\theta$) =({(sin $\theta$+cos $\theta$)-1}{(sin $\theta$+cos $\theta$)+1})/(sin $\theta$ cos $\theta$) =((sin $\theta$+cos $\theta$)^2-(1)^2)/(sin $\theta$ cos $\theta$) =((sin $\theta$+cos $\theta$)^2-(1)^2)/(sin $\theta$ cos $\theta$) =((sin^2 $\theta$+cos^2$\theta$+2 sin $\theta$cos $\theta$)-1)/(sin $\theta$ cos $\theta$) =((sin ^2$\theta$+cos^2$\theta$)+2 sin$\theta$ cos $\theta$-1)/(sin $\theta$cos $\theta$) = (1+2 sin $\theta$ cos$\theta$-1)/(sin$\theta$ cos $\theta$) =( 2 sin $\theta$ cos $\theta$)/(sin $\theta$ cos $\theta$) =2`

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