If tan^2theta+cot^2theta=2 theta is an acute angle then what is the value of tan^3theta+cot3theta
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Answer:
Step-by-step explanation:
** 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
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Step-by-step explanation:
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