Answer:
Step-by-step explanation:
a). [tex]\text{cos}^4(\frac{\theta}{6})-\text{sin}^4(\frac{\theta}{6})=\text{cos}\frac{\theta}{3}[/tex]
By solving left hand side of the equation,
= [tex][\text{cos}^2(\frac{\theta}{6})-\text{sin}^2(\frac{\theta}{6})][\text{cos}^2(\frac{\theta}{6})+\text{sin}^2(\frac{\theta}{6})][/tex]
= [tex][\text{cos}^2(\frac{\theta}{6})-\text{sin}^2(\frac{\theta}{6})](1)[/tex] [Since, cos²a + sin²a = 1]
= [tex]\text{cos}\frac{\theta}{3}[/tex] [Identity used → cos²a - sin²a = cos(2a)]
Hence, left hand side of the given equation = Left hand side of the equation.
