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please solve this explaining every step i am hell confused?

please solve this explaining every step i am hell confused?
tan^{6}x - 1 = 3tan^{4}x - 3tan^{2}x
 

Grade:11

2 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:Hello student, please find answer to your question
tan^{6}x - 1 = 3tan^{4}x - 3tan^{2}x
(tan^{2}x)^{3} - 1 = 3tan^{2}x(tan^{2}x - 1)
x^{3} - 1 = (x-1)(x^{2}+x+1)
(tan^{2}x - 1)(tan^{4}x + tan^{2}x + 1) = 3tan^{2}x(tan^{2}x - 1)
(tan^{4}x + tan^{2}x + 1) = 3tan^{2}x
tan^{4}x - 2tan^{2}x + 1 = 0
(tan^{2}x - 1)^{2} = 0
\Rightarrow tanx = \pm 1
Cheers!
rashmi
22 Points
9 years ago
ththanks a lot sir .. now i understood , sry for askingsame ques again but i am not so good at trigonometry just a beginner so cant understand easily thanks 
and ya cheering....
thanku once again...

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