Add or subtract? Simplify your answer if possible. Leave your answer in terms of sin theta and/or cos theta sin theta + 1/cos theta

#sin theta + 1/cos theta#

1 Answer
Jul 12, 2018

Let

#E(theta) = sintheta+1/costheta#

#E(theta) = (sinthetacostheta+1)/costheta#

This form is already in terms of #sintheta# and #costheta#, but let's continue anyway.

Recognizing that #1# is nothing more than #sin^2theta+cos^2theta#, we have

#E(theta) = (sin^2theta+sinthetacostheta+cos^2theta)/costheta#

We know that

#a^3-b^3=(a-b)(a^2+ab+b^2) => a^2+ab+b^2=(a^3-b^3)/(a-b)#

#E(theta) = ((sin^3theta-cos^3theta)/(sintheta-costheta))/costheta=(sin^3theta-cos^3theta)/(sinthetacostheta-cos^2theta)#

This is another possible answer.