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Identity is cosec square tita-cot square tita=1
(cosec tita+cot tita)(cosec tita-cot tita)=1
p(cosec tita-cot tita)=1
cosec tita-cot tita=1/p
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cosecФ + cotФ = p
we know that 
cosec²Ф - cot²Ф = 1
⇒(cosecФ + cotФ)(cosecФ - cotФ) = 1

⇒p x (cosecФ - cotФ) = 1

⇒(cosecФ - cotФ) = 1/p

(cosecФ - cotФ) = \frac{1}{p}
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