Evaluate the integral:
{eq}\displaystyle \int \frac {1}{cos \ \theta - 1} \ d \theta {/eq}.
Question:
Evaluate the integral:
{eq}\displaystyle \int \frac {1}{cos \ \theta - 1} \ d \theta {/eq}.
Double Cosine
The trigonometric identity for the double cosine of an angle {eq}x {/eq} can be expressed in terms of the sine and the cosine of the full angle as,
{eq}\cos 2x=\cos^2 x-\sin^2 x {/eq}.
Moreover, mixing this result with the fundamental trigonometric identity {eq}\sin^2 x+\cos^2 x=1 {/eq} allows us to eliminate one of the trigonometric functions (either the sine or the cosine),
{eq}\cos 2x=1-2\sin^2 x=2\cos^2 x-1 {/eq}.
Answer and Explanation:
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View this answerTo compute the integral,
{eq}I= \displaystyle \int \dfrac{d\theta}{\cos \theta -1} {/eq},
we employ the trigonometric identity,
{eq}\cos...
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Chapter 23 / Lesson 1Learn to define basic trigonometric identities. Discover the double-angle, half-angle, and other identities. Learn how to use trigonometric identities. See examples.