If cosec A + cot A = 7, then cosec A is equal to:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 25/7.
cosec2A - cot2A = 1
⇒(cosec A + cot A)(cosec A - cot A) = 1
⇒ 7(cosec A - cot A) = 1
⇒ cosec A - cot A = 1/7 .....(1)
Also, cosec A + cot A = 7 .....(2)
From two equations, we get
2cosec A = 7 + 1/7 = 50/7
⇒ cosec A = 25 / 7