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

1 Answer
Aug 25, 2016

See below.

Explanation:

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!