Indefinite Integration
Integration of Trigonometric Functions
Grade 12
Question:
<p>Evaluate: <equation>\int \frac{\cot x}{(\cos x)^{2005}} dx</equation></p>
<p>(a) <equation>-\frac{\tan x}{(\cos x)^{2005}} + C</equation></p>
<p>(b) <equation>\frac{\cot x}{(\cos x)^{2005}} + C</equation></p>
<p>(c) <equation>-\frac{\tan x}{(\cos x)^{2005}} + C</equation></p>
<p>(d) <equation>-\frac{\cot x}{(\cos x)^{2005}} + C</equation></p>
Step-by-Step Solution
Key Concept: Use trigonometric identities and substitution to evaluate the integral of trigonometric functions.
<p><strong>Step 1:</strong> Rewrite the integrand using trigonometric identities.</p><p><strong>Step 2:</strong> Apply substitution or standard integration techniques.</p><p>∴ Answer is (a).</p>
Correct Answer: A