Proof trigonometry identities.\csc(x)+\cot(x)=\frac{1}{\csc(x)-\cot(x)}

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Answered question

2021-09-08

Proof trigonometry identities.
csc(x)+cot(x)=1csc(x)cot(x)

Answer & Explanation

FieniChoonin

FieniChoonin

Skilled2021-09-09Added 102 answers

Let as consider the given function,
L.H.S.=R.H.S.
First to solve R.H.S.,
1csc(x)cot(x)
Use the following trigonometric identity: 1=cot2(x)+csc2(x)
1csc(x)cot(x)=cot2(x)+csc2(x)cot(x)+csc(x)
Apply Difference of Two Squares Formula:
csc2(x)cot2(x)=(csc(x)+cot(x))(csc(x)cot(x))
1csc(x)cot(x)=(csc(x)+cot(x))(csc(x)cot(x))cot(x)+csc(x)
1csc(x)cot(x)=csc(x)+cot(x)
Hence, LHS=RHS
Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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