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

Question

$sin theta + 1/cos theta$

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Answer 1 · 2018-07-12T18:40:52

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.