Problem 357

{{searchResults.length}} results for “{{searchWords}}” No results found for “{{searchWords}}” × back to contents

§{{x[0]}} {{x[1]}}

Table of Contents

Problem 357: (2002 AMC12P, 10)

Let $f_n (x) = \text{sin}^n x + \text{cos}^n x.$ For how many $x$ in $[0,\pi]$ is it true that \[6f_{4}(x)-4f_{6}(x)=2f_{2}(x)?\] $\text{(A) }2 \qquad$ $ \text{(B) }4 \qquad$ $ \text{(C) }6 \qquad$ $ \text{(D) }8 \qquad$ $ \text{(E) more than }8$

Solution

Exercise 357: Solution

Let $f_n(x)=\sin^nx+\cos^nx$. For how many $x$ in $[0,\pi]$ is it true that $9f_4(x)-6f_6(x)=3f_2(x)$?

Search Go to Prev Next

Contact Us