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  • ?Prove that : an^2 heta+cot^2 heta +2=sec^2 heta.csc^2 heta

?Prove that : an^2 heta+cot^2 heta +2=sec^2 heta.csc^2 heta

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an^2 heta+cot^2 heta +2=sec^2 heta .csc^2 heta\*Take;LHS,\* Rightarrow an^2 heta+cot^2 heta +2 \* We;know;that; 1+ an^2 heta =sec^2 heta;and;1+cot^2 heta = csc^2 heta\* Rightarrow ( an^2 heta+1)+(cot^2 heta +1)\* Rightarrow sec^2 heta + csc^2 heta=frac1sin^2 heta+frac1cos^2 heta\* ecause csc heta = frac1sin heta,;; sec heta =frac1cos heta\*Rightarrow fracsin^2 heta + cos^2 hetasin^2 heta. cos^2 heta\* We;also; know;that;sin^2 heta +cos^2 heta+1\* Rightarrow frac1sin^2 heta. cos^2 heta=sec^2 heta. csc^2 heta\* Hence, LHS=RHS

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Deependra Verma

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