Proof trigonometric identities.\sec(x)+\tan(x)=\frac{\cos(x)}{1-\sin(x)}

Rivka Thorpe

Rivka Thorpe

Answered question

2021-09-12

Proof trigonometric identities.
sec(x)+tan(x)=cos(x)1sin(x)

Answer & Explanation

Ayesha Gomez

Ayesha Gomez

Skilled2021-09-13Added 104 answers

The given equation is sec(x)+tan(x)=cos(x)1sin(x)
Let choose sec(x)+tan(x) to prove cosx1sinx to prove the identity.
secx+tanx=1cosx+sinxcosx
(secx=1cosx,tanx=sinxcosx)
=1+sinxcosx
=1+sinxcosxcosxcosx
=(1+sinx)cosxcos2x
On further simplification,
secx+tanx=(1+sinx)cosx(1sin2x)
=(1+sinx)cosx12sin2x
=(1+sinx)cosx(1+sinx)(1sinx)
=cosx(1sinx)
Hence, the given identity is proved.
Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-11Added 2605 answers

Answer is given below (on video)

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