Question

Review the proof step statement 1 cos(2x) = 1-sin^2(x)

Answer 1

Option (3)

Explanation:

Correct steps for the proof are,

Step Statement

1 cos(2x) = 1 - 2sin²(x)

2 Let 2x = θ

3 x =
`(\theta)/(2)`

4
`\text{cos}\theta = 1 - 2\text{sin}^2((\theta)/(2) )`

5
`\text{cos}\theta-1 =-2\text{sin}^2((\theta)/(2) )`

6
`1-\text{cos}\theta =2\text{sin}^2((\theta)/(2) )`

7
`\frac{1-\text{cos}\theta}{2} =\text{sin}^2((\theta)/(2) )`

8
`\pm \sqrt{\frac{1-\text{cos}\theta}{2} }=\text{sin}((\theta)/(2) )`

There is a mistake in step 6.

Therefore, Option (3) will be the answer.