Question

If tan2theta+cot2theta=2, theta is an acute angle, then tan3theta
+cot3theta is equal to________.

Answer 1

Answer:

x = theta

tan^2x+cot^2x=2

tan^2x+1/tan^2x=2

tan^4x+1=2tan^2x

tan^4x-2tan^2x+1=0

(tan^2x-1)(tan^2x-1)=0

tan^2x=1

tanx=1

cotx=1

use sum of cubes formula

tan^3x+cot^3x

=(tanx+cotx)(tan^2x-tanxcotx+cot^2x)

=(1+1)(1-1+1)=2

please mark as a brainlist