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How to find the general solution of tan^2x = 3cosec^2 x-1?

How to find the general solution of tan^2x = 3cosec^2 x-1?

Grade:11

2 Answers

Arun
25750 Points
5 years ago
Dear Purva
 
1 + tan^2 x = 3 cosec^2 x
 
sec^2x = 3 cosec^2 x
tan^2 x = 3
 
x = n* pi ± pi/3
 
Regards
Arun (askIITians forum expert)
sahil
13 Points
one year ago
tan^2 x = 3 cosec^2 x – 1
→ 1+ tan^2 x = 3 Cosec^2 x
→ sec^2 x = 3 cosec^2x 
                                 [∵ sec^2x = 1+ tan^2x]
→ 1/cos^2 x = 3 (1/sin^2 x)
                                  [∵ sec^2 x = 1/cos^2 x  &
                                       cosec^2 x = 1/sin^2 x]
→ (1/cos^2 x) (1/sin^2 x/1) = 3
→ sin^2 x/cos^2 x = 3
                                   [∵ tan^2 x = sin^2 x/cos^2 x]
→ tan^2 x = 3
 ∴  x= n⊼ ± ⊼/3
 

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