How do you verify the identity $(tanx+secx)(1-sinx)=cosx$ ?

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Answer 1 · 2016-08-26T20:06:03

See below.

Use the following identities to simplify the left-hand side:

• $tanbeta = sinbeta/cosbeta$

• $secbeta = 1/cosbeta$

Start the simplification process:

$(sinx/cosx + 1/cosx)(1 - sinx) = cosx$

$((sinx + 1)/(cosx))(1 - sinx) = cosx$

$(1 - sin^2x)/cosx = cosx$

Now, rearrange the pythagorean identity $sin^2beta + cos^2beta = 1$ for $cos^2beta$ to get $cos^2beta = 1- sin^2beta$ . Applying this to our problem:

$cos^2x/cosx = cosx$

$((cosx)(cosx))/cosx = cosx$

$(cancel(cosx)cosx)/cancel(cosx) = cosx$

$cosx = cosx$

Identity proved!!

Hopefully this helps!

How do you verify the identity (tanx+secx)(1-sinx)=cosx(tanx+secx)(1-sinx)=cosx?