Check the solution to "What is sec⁡θ+cos⁡θ in terms of sin⁡θ?"

supermamanswtk

Answered question

2022-12-30

What is

\sec θ + \cos θ

in terms of

\sin θ

dalagudurps8

Beginner2022-12-31Added 7 answers

To rewrite the expression in terms of

\sin θ

, use the reciprocal identity mentioned above to make the expression simpler:

\sec θ + \cos θ

= \frac{1}{\cos θ} + \cos θ

= \frac{1 + \cos θ (\cos θ)}{\cos θ}

= \frac{1 + \cos^{2} θ}{\cos θ}

= \frac{1 + (1 - \sin^{2} θ)}{\cos θ} \Leftarrow \cos^{2} θ = 1 - \sin^{2} θ

= \frac{2 - \sin^{2} θ}{\cos θ}

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