Mathematics

The key is recognizing that $\sec\theta$ is just the reciprocal of $\cos\theta$, so dividing by it is the same as multiplying by $\cos\theta$. Once you rewrite the fraction using basic trig definitions, the $\cos\theta$ terms will interact in a way that leaves you with one of the fundamental ratios. This is a great reminder that reciprocal identities are your friends when simplifying.

The key is recognizing that $\sec\theta$ is just the reciprocal of $\cos\theta$, so dividing by it is the same as multiplying by $\cos\theta$. Once you rewrite the fraction using basic trig definitions, the $\cos\theta$ terms will interact in a way that leaves you with one of the fundamental ratios. This is a great reminder that reciprocal identities are your friends when simplifying.