Question

Question #cf786

Answer 1

see below

Explanation:

Use the following Properties:

1. Pythagorean Properties

   `1+cot^2 x = csc^2 x`

   `1+tan^2x=sec^2x`

   `cos^2x+sin^2x=1`

2. Reciprocal Properties
   `csc x = 1/sinx`

   `sec x = 1/cos x`

Left hand Side :

`(1-cotx)^2 + (1-tan x)^2=1-2cotx+cot^2x+1-2tan^2x+tan^2x`

`=1+cot^2x-2cotx-2tanx+1+tan^2x`

`=csc^2x-2(cotx+tanx)+sec^2x`

`=csc^2x-2(cosx/sinx+sinx/cosx)+sec^2x`

`=csc^2x-2((cos^2x+sin^2x)/(sinx cosx))+sec^2x`

`=csc^2x-2(1/(sinx cosx))+sec^2x`

`=csc^2x-2(1/sinx 1/cosx)+sec^2x`

`=csc^2x-2 1/sinx 1/cosx+sec^2x`

`=csc^2x-2 cscx sec x+sec^2x`---> factor

`=(cscx-secx)(cscx-secx)`

`=(cscx-secx)^2`

`:.=` Right Hand Side