Question

1+cotx+cosecx/1-cotx+cosecx=​

Answer 1

Answer:

hey mate

Step-by-step explanation:

here is your answer

1+cotx+cosecx/1-cotx+cosecx= 1 + cosx / sin X

solution

$\frac{1 + \cot \: x + \csc \: x }{1 - \cot \: x \: + \csc \: x } = \frac{1 + ( \cot \: x + \csc \: x) }{1 - ( \cot \: x \: - \: \csc \: x) }$

Rationalising method

$\frac{(1 \: + ( \cot \: x \: + \csc \: x)) \: (1 + ( \cot \: x - \csc \: x)) }{(1 - ( \cot \: x \: - \csc \: x)) \: (1 \: + \: ( \cot \: x - \csc \: x ) }$

solving the numerator

(1 + (cot X + cosec X )) (1 + (cot X - cosec X))

= 1 + cot X - cosec X + cot X + cosec X + (cot² X - cosec²x)

= 1 + 2 cotx - 1

= 2 cot X

solving denominator

(1 - (cot X - cosec X )) ( 1 + ( cot X - cosec X))

= 1 - (cot X - cosec x)²

= (cosec²x - cot²x) - (cot X - cosec X )²

= (cosec X - cot X) (cosec X + cot X - cosec X + cot X)

= 2cotx (cosecx - cotx)

use simple form

= 2 cotx/2cot X × (cosec X - cotx)

$\frac{1}{ \csc\: x - \cot \: x }$

by rationalising method

$\frac{ \csc \: + \cot \: x }{( { \csc \: \: }^{2} x - { \cot \: }^{2} x)}$

$\csc \: x \: + \: \cot \: x$

$\frac{1}{ \sin \: x \: } + \: \frac{ \cos \: x }{ \sin \: x }$

$\frac{1 \: + \: \csc \: x}{ \sin \: x }$

$thanku$