Question

If cosecA-cotA=3/2,find cosA and also the quadrant in which A line?

Answer 1

We know that, 
cosec²A-cot²A=1
or, (cosecA+cotA)(cosecA-cotA)=1
or, (cosecA+cotA)(3/2)=1
or, cosecA+cotA=2/3 -----------------------(1)
cosecA-cotA=3/2 ----------------------------(2)
Adding (1) and (2) we get,
2cosecA=2/3+3/2
or, 2cosecA=13/6
or, cosecA=13/12
or, sinA=12/13
∴, cosA=√(1-sin²A) 
[∵, sin²A+cos²A=1]
or, cosA=√(1-144/169)
or, cosA=√{(169-144)/169}
or, cosA=√(25/169)
or, cosA=+-5/13
Now, by subtracting (2) from (1) we get, cotA=-5/12
∴, A lies either in 2nd or in 4th quadrant.
∴, cosA=-5/13 (if A lies in 2nd quadrant)
or, cosA=5/13 (if A lies in 4th quadrant)

Answer 2

Answer:

5/13 is the correct answer