Question

if cosec theta + cot theta = x , then show that cosec theta - cot theta = 1/x

Answer 1

Thank you for asking this question. Here is your answer:

We will let theta = y

We have an identity that is cosec²(Y)-cot²(Y)=1

With the help of this now we will find the answer:

cosec²(Y)-cot²(Y)=1

[cosec(Y)+cot(Y)][cosec(Y)-cot(Y)]=1            {since a²-b²=[a+b][a-b]}

[cosec(Y)+cot(Y)][x]=1                                 {from given}

cosec(Y)+cot(Y)=1/x

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