Question

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

Answer 1

Hello Friend,

Here,

→ cosec A - cot A = 3/2 ----(1)

→ We know that,

cosec²A - cot²A = 1

So, (cosec A + cot A)(cosec A - cot A) = 1

So, (cosec A + cot A)(3/2) = 1 (From (1))

So, cosec A + cot A = 2/3 ----(2)

→ Now , add (1) and (2)
So,

cosec A - cot A = 3/2
cosec A + cot A = 2/3
----------------------------------
So, 2 cosec A = (3/2) + (2/3)

So, 2 cosec A = 13/6
So, cosec A = 13/12
So, sin A = 1/cosec = 12/13

→ Now, we have sin A = 12/13

sin A is positive. This means that A lies in either First or Second Quadrant.

We can find cot A easily to check which quadrant A lies in.

Putting cosec A = 13/12 in (2)
So, cosec A + cot A = 2/3
So, 13/12 + cot A = 2/3
So, cot A = 2/3 - 13/12
So, cot A = (8-12)/12
So, cot A = -5/12

• Now, cot A is negative. So A can either be in Second or Fourth Quadrant.

But, as sin A is also positive , A must lie in Second Quadrant.

→ Now,
cot A = cos A/sin A
So, cos A = cot A × sin A
So, cos A = (-5/12) × (12/13)
So, cos A = -5/13

→ Thus, cos A = -5/13, and A lies in Second Quadrant.


Hope it helps.

Purva
@Purvaparmar1405
Brainly.in