Question

This question has been bothering me for some time now, im not sure what i’m doing wrong

Answer 1

`\begin{gathered} sin(\theta)=(√(2))/(5) \\ sin(2\theta)=2sin(\theta)cos(\theta) \\ cos(2\theta)=cos^2(\theta)-sin^2(\theta) \\ cos(\theta)=? \\ sin^2(\theta)+cos^2(\theta)=1 \\ cos^2(\theta)=1-sin^2(\theta) \\ cos^2(\theta)=1-((√(2))/(5))^2 \\ cos^2(\theta)=1-(2)/(25) \\ cos^2(\theta)=(23)/(25) \\ cos(\theta)=\sqrt{(23)/(25)} \\ cos(\theta)=(√(23))/(5) \\ Hence \\ s\imaginaryI n(2\theta)=2s\imaginaryI n(\theta)cos(\theta) \\ s\imaginaryI n(2\theta)=(2)((√(2))/(5))((√(23))/(5)) \\ s\imaginaryI n(2\theta)=(2√(46))/(25) \\ \\ cos(2\theta)=cos^2(\theta)-s\imaginaryI n^2(\theta) \\ cos(2\theta)=(23)/(25)-(2)/(25) \\ cos(2\theta)=(21)/(25) \end{gathered}`