Question

prove 1/cosec x +cot x-1/sinx=1/sinx-1 cosecx -cotx

Answer 1

Answer:

$\frac{1}{cosecx-cotx}-\frac{1}{sinx}$$=$$\frac{1}{sinx}-\frac{1}{cosecx+cotx}$

Step-by-step explanation:

Concept:

$cosec^2\theta-cot^2\theta=1$

L.H.S

$=\frac{1}{cosecx-cotx}-\frac{1}{sinx}\\\\=\frac{cosec^2x-cot^2x}{cosecx-cotx}-cosecx\\\\=\frac{(cosecx-cotx)(cosecx+cotx)}{cosecx-cotx}-cosecx\\\\=cosecx+cotx-cosecx\\\\=cotx..........(1)$

R.H.S

$=\frac{1}{sinx}-\frac{1}{cosecx+cotx}\\\\=cosecx-\frac{cosec^2x-cot^2x}{cosecx+cotx}\\\\=cosecx-\frac{(cosecx-cotx)(coseecx+cotx)}{cosecx+cotx}\\\\=cosecx-(cosecx-cotx)\\\\=cosecx-cosecx+cotx\\\\=cotx..........(2)$

From (1) and (2)

L.H.S=R.H.S

Answer 2

Answer:

here is your Answer

Step-by-step explanation:

mark me as brainliest