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1+tan2A/1+cot2A = (A) sec2 A (B) -1 (C) cot2A (D) tan2A

1+tan2A/1+cot2A =
(A) sec2 A (B) -1 (C) cot2A (D) tan2A

Grade:12

3 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

option (D) is correct.

Justification:
We know that,
tan^2 A =1/cot^2 A
Now, substitute this in the given problem, we get

1+tan^2 A/1+cot^2 A
= (1+1/cot^2 A)/1+cot^2 A
= (cot^2 A+1/cot^2 A)×(1/1+cot^2 A) = 1/cot^2 A = tan^2 A
So, 1+tan^2 A/1+cot^2 A = tan^2 A
Thanks
surya prakash
17 Points
3 years ago
Welcome to askIITians,
 
we know that 1 + Cot 2A =( 1 + Tan 2A ) / Tan 2A
 
Given that  (1 + Tan 2A )/ ( 1 + Cot 2A)
 
             = (1 + Tan 2A) (Tan 2A) / ( 1 + Tan 2A)
 
              = Tan 2 A 
 
Answer  : Option (D) 
 
Thank You
 
 
Sudhir
15 Points
3 years ago
 
Dear student,
We know that Cot 2A = 1/Tan 2A .....(I)
 
Your questions is :
1+Tan 2A/ 1+ Cot 2A
= 1+Tan 2A / 1+ (1/Tan 2A).   From eq.(I)
Taking LCM as Tan 2A in the denominator. We get,
= (Tan 2A)(1+Tan 2A)/ (1+Tan 2A)
= Tan 2A   
 
Correct option is (D)
 
 

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