Show that `1+cot^2alpha/(1+cosecalpha)=cosec alpha` – InterviewSolution

InterviewSolution

1.	Show that `1+cot^2alpha/(1+cosecalpha)=cosec alpha`
Answer» LHS = `1+ (cot^(2)alpha)/(1+"cosec"alpha)=1+(cos^(2)alpha//sin^(2)alpha)/(1+1//sinalpha)` `[therefore cottheta=(costheta)/(sintheta)` and `"cosec"theta=1/(sintheta)]` `=1+ (cos^(2)alpha)/(sinalpha(1+sin alpha))` `=(sinalpha + 1)/(sinalpha(sinalpha+1))=1/sinalpha` `[therefore "cosec"theta=1/sintheta]` `="cosec"alpha=RHS`

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