Answer:
Option (3)
Step-by-step explanation:
Correct steps for the proof are,
Step Statement
1 cos(2x) = 1 - 2sin²(x)
2 Let 2x = θ
3 x = [tex]\frac{\theta}{2}[/tex]
4 [tex]\text{cos}\theta = 1 - 2\text{sin}^2(\frac{\theta}{2} )[/tex]
5 [tex]\text{cos}\theta-1 =-2\text{sin}^2(\frac{\theta}{2} )[/tex]
6 [tex]1-\text{cos}\theta =2\text{sin}^2(\frac{\theta}{2} )[/tex]
7 [tex]\frac{1-\text{cos}\theta}{2} =\text{sin}^2(\frac{\theta}{2} )[/tex]
8 [tex]\pm \sqrt{\frac{1-\text{cos}\theta}{2} }=\text{sin}(\frac{\theta}{2} )[/tex]
There is a mistake in step 6.
Therefore, Option (3) will be the answer.
