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If cosecA – cotA = 3 then cosecA + cotA = ?
Question

If cosecA – cotA = 3 then cosecA + cotA = ?

A.

13\frac{1}{3}​​

B.

12\frac{1}{2}​​

C.

15\frac{1}{5}​​

D.

32\frac{3}{2}​​

Correct option is A

Given:
cosecA – cotA = 3
Formula Used:
Trigonometric identity: cosec²A - cot²A = 1
Difference of squares factorization: a² - b² = (a + b)(a - b)
Solution:
We know that ,

cosec²A - cot²A = 1.
(cosecA + cotA)(cosecA - cotA) = 1
(cosecA + cotA) × 3 = 1
cosecA + cotA = 13\frac{1}{3}​​










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