Question

Question #63bfa

Answer 1

see below

Explanation:

Use the following Properties

1. Double Argument Property
   `cos 2theta=1-2sin^2theta`

2. Reciprocal Property
   `sin theta = 1/csc theta`

3. Pythagorean Property
   `1+cot^2theta=csc^2 theta`

Left Hand Side:

`1-cos 2 theta=1-[1-2sin^2theta]`

`=1-1+2sin^2theta`

`=cancel(1-1)+2sin^2theta`

`=2sin^2 theta`

`=2(1/csc^2 theta)`

`=2/csc^2 theta`

`=2/(1+cot^2 theta)`

`:.=` Right Hand Side