Prove the following identity

cosec (theta) + tan (theta) = 1 / [cosec (theta) - tan (theta)]

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- October 23rd 2011, 09:26 AMIlsaTrigonometric Identities
Prove the following identity

cosec (theta) + tan (theta) = 1 / [cosec (theta) - tan (theta)] - October 23rd 2011, 10:05 AMSammySRe: Trigonometric Identities
- October 23rd 2011, 10:40 PMIlsaRe: Trigonometric Identities
cosec (theta) + tan (theta)

= 1 / sin (theta) + (sin (theta)/cos (theta))

= [cos (theta) + sin ^2 (theta) ] / sin (theta) cos (theta)

I require help for further steps

If I substitute sin^2 (theta) = 1 - cos^2 (theta)

then:

= [cos (theta) + 1 - cos^2 (theta) ] / sin (theta) cos (theta)

With the above expression I am unable to prove the identity.

This is where I'm stuck. - October 24th 2011, 12:06 AMsbhatnagarRe: Trigonometric Identities
- November 4th 2011, 06:06 AMSorobanRe: Trigonometric Identities
Hello, Ilsa!

The statement is not true. .Is there a typo?

Quote:

. This is true

Multiply the right side by

. .