Prove the following trigonometric identities- cosec-A-cosec-A-1-cosec-A-cosec-A-1-2sec2A

Ans: To prove, (cosecA)(cosecA−1)+(cosecA)(cosecA+1)(cosecA)(cosecA−1)+(cosecA)(cosecA+1) = 2sec2 A Considering left hand side (LHS), = (cosecA)(cosecA+1+cosecA ...

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Standard X

Mathematics

Trigonometric Identities

Prove the fol...

Question

Prove the following trigonometric identities:

$\frac{c o s e c A}{c o s e c A - 1} + \frac{c o s e c A}{c o s e c A + 1} = 2 s e c^{2} A$

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Solution

Ans:

To prove,

(cosecA)(cosecA−1)+(cosecA)(cosecA+1)(cosecA)(cosecA−1)+(cosecA)(cosecA+1) = 2sec²A

Considering left hand side (LHS),

= (cosecA)(cosecA+1+cosecA−1)(cosec2A−1))(cosecA)(cosecA+1+cosecA−1)(cosec2A−1))

= (2cosec2A)cot2A(2cosec2A)cot2A

= (2sin2A)sin2A.cos2A(2sin2A)sin2A.cos2A

= 2cos2A2cos2A

= 2sec2A2sec2A

Therefore, LHS = RHS

Hence proved

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Prove the following trigonometric identities: cosec Acosec A−1+cosec Acosec A+1=2sec2A

Prove the following trigonometric identities:

$\frac{c o s e c A}{c o s e c A - 1} + \frac{c o s e c A}{c o s e c A + 1} = 2 s e c^{2} A$