Answer:
Error in step (5)
Step-by-step explanation:
Steps Statements
1 cos(2x) = 2cosx - 1
2 Let (2x) = θ
3 Then x = [tex]\frac{\theta }{2}[/tex]
4 cos(θ) = [tex]2\text{cos}^2{\theta}-1[/tex]
5 cos(θ) + 1 = [tex]2\text{cos}^2{\frac{\theta}{2}}[/tex]
6 [tex]\frac{1+\text{cos}\theta }{2}=cos^{2}\frac{\theta }{2}[/tex]
7 [tex]\text{cos}^{2}\frac{\theta }{2}=\frac{1+\text{cos}\theta }{2}[/tex]
8 [tex]\text{cos}(\frac{\theta }{2})=\pm \sqrt{\frac{1+cos(\theta)}{2} }[/tex]
By comparing the solution given in the picture attached with the solution above,
Step 5 has error.
There should be [cos(θ) + 1 = [tex]2\text{cos}^2({\frac{\theta}{2}})[/tex]] in place of [-1 + cos(θ) = [tex]2\text{cos}^2({\frac{\theta}{2}})[/tex]]
