Question

If cotA/1+cosecA-cotA/1-cosecA=K/cosA,then find the value of K​

Answer 1

GIVEN

$\dfrac{cotA}{1+cosecA}-\dfrac{cotA}{1-cosecA}=\dfrac{k}{cosA}$

TO FIND

The value of k

EXPLANATION

in the attachment

FORMULAS

$= > (a + b)(a - b) = {a}^{2} - {b}^{2}$

$= > cotx = \dfrac{cosx}{sinx}$

$= > cosecx = \dfrac{1}{sinx}$

$= > {sin}^{2} x + {cos}^{2} x = 1 \\ \\ {cos}^{2} x = 1 - {sin}^{2} x$

EXTRA INFORMATION

$= > {sec}^{2} x - {tan}^{2} x = 1 \\ \\ = > {cosec}^{2} x - {cot}^{2} x = 1$

Answer 2

Answer:

k = 2

Step-by-step explanation:

Multiply by cos A and factor out cot A.  Also handier to change signs of numerator and denominator in second term:

k = cos A cot A ( 1 / ( cosec A + 1 )   +   1 / ( cosec A - 1 ) )

Change everything to cos A and sin A.  Distribute the 1 / sin A (from the cot A) over the terms:

k = cos² A ( 1 / ( 1 + sin A )  +  1 / ( 1 - sin A ) )

= cos² A ( 1 - sin A + 1 + sin A ) / ( 1 - sin² A )

= cos² A ( 2 ) / cos² A

= 2