Question

cosecA+cot A=2/3
COS A=??
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Answer 1

Answer:

Step-by-stHello 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.....plzz mark me on brainliests