CBSE Class 11-science Answered

1/ tan3A-tanA    -        1/cot3A-cotA  =  cot2A 

1/ 1/ cot3A - 1/ cotA  -  1/ cot3A - cotA

cotA cot3A/ cotA - cot3A   -  1/ cotA - cot3A

1 + cotA cot3A / cotA - cot3A

(1 + 1/ tanA.tan3A )/ (1/ tanA - 1/ tan3A)

(tanA tan3A +1)/ (tan3A - tanA )  

{ tanA ( 3 tanA - tan³A/ 1-3tan²A) + 1} / {( 3 tanA - tan³A)/1 - 3tan²A} - tanA 

                                                                                   tan3A = 3 tanA - tan³A/ 1-3tan²A

(1 - tan ⁴ A)/ (2 tan A + 2tan³A)  = (1 - tan²A)/ 2 tanA

 = ( 1 - tan²A)( 1+tan²A)/ 2tanA ( 1+tan²A) =  ( 1 - tan²A)/ 2tanA

 = (cot² A - 1)/2 cot2A  = cot2A

                               Proved