Given:
[tex]cos300^{\degree}[/tex]
Required:
We need to determine the exact value of the given expression.
Explanation:
[tex]We\text{ know that }cos2\theta=2cos^2\theta-1.[/tex][tex]Substitute\text{ }\theta=150\degree\text{ in the equation.}[/tex]
[tex]cos(2\times150)=2cos^2(150\degree)-1.[/tex]
[tex]cos(300\degree)=2cos^2(150\degree)-1.[/tex][tex]\text{We know that }cos2\theta=1-2sin^2\theta.[/tex]
[tex]Substitute\text{ }\theta=150\degree\text{ in the equation.}[/tex]
[tex]cos(2\times150)\degree=1-2sin^2(150)\degree.[/tex]
[tex]cos(300)\degree=1-2sin^2(150)\degree.[/tex]
Final answer:
[tex]cos(300\degree)=2cos^2(150\degree)-1.[/tex]
[tex]cos(300)\degree=1-2sin^2(150)\degree.[/tex]
