How do you prove $(sinx+cosx)/(secx+cscx)=sinx/secx$ ?

Question

13149 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-25T14:59:53

See below.

Apply the following identities:

• $sectheta = 1/costheta$

• $csctheta = 1/sintheta$

Now, simplify both sides using the given identities:

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

$(sinx + cosx)/((sinx + cosx)/(sinxcosx)) = sinxcosx$

$sinx + cosx xx (sinxcosx)/(sinx + cosx) = sinxcosx$

$cancel(sinx + cosx) xx (sinxcosx)/(cancel(sinx+cosx)) = sinxcosx$

$sinxcosx = sinxcosx$

Identity proved!!

Hopefully this helps!

How do you prove (sinx+cosx)/(secx+cscx)=sinx/secx(sinx+cosx)/(secx+cscx)=sinx/secx?