SOLUTION: if tan^2 theta + cot^2 theta = 2 theta is an acute angle then tan^3 theta + cost^3 theta is equal to a)2 b)3 c)4 d)8

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Question 784542: if tan^2 theta + cot^2 theta = 2 theta is an acute angle then tan^3 theta + cost^3 theta is equal to
a)2
b)3
c)4
d)8
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
if tan^2 theta + cot^2 theta = 2 theta is an acute angle then tan^3 theta + cost^3 theta is equal to
***
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(ans:a)