Question

Iftan????=1/√7, then cosec²????-sec²????/cosec²????+sec²????=
A. 5/7
B. 3/7
C. 1/12
D. 3/4

Answer 1

C . 1 / 12

This is the correct answer.

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Answer 2

cosec²A -sec²A /cosec²A + sec²A = 3/4

Step-by-step explanation:

Given: tan A = 1/√7  

Find: cosec²A -sec²A /cosec²A + sec²A

Solution:

We know that Sec²A = 1 + (1/√7)² = 1 + 1/7 = 8/7

 cosec²A -sec²A /cosec²A + sec²A

 = (1/Sin²A - 1/Cos²A) / (1/Sin²A + 1/Cos²A)  

 = (Cos²A - Sin²A) / Sin²A.Cos²A / (Sin²A + Cos²A)/Sin²A.Cos²A

 = Cos²A - Sin²A / 1

 = Cos²A - Sin²A

 = 1/sec²A - (1 - 1/sec²A)

 = 1/(8/7) - (1 - 1/(8/7))

 = 7/8 - 1 + 7/8

 = 7/4 - 1

 = (7 - 4) / 4

 = 3/4

Therefore value of cosec²A -sec²A /cosec²A + sec²A = 3/4