Question

Can anyone help me with any one of these questions please ​

Answer 1

Explanation:

a).
`\text{cos}^4((\theta)/(6))-\text{sin}^4((\theta)/(6))=\text{cos}(\theta)/(3)`

By solving left hand side of the equation,

=
`[\text{cos}^2((\theta)/(6))-\text{sin}^2((\theta)/(6))][\text{cos}^2((\theta)/(6))+\text{sin}^2((\theta)/(6))]`

=
`[\text{cos}^2((\theta)/(6))-\text{sin}^2((\theta)/(6))](1)` [Since, cos²a + sin²a = 1]

=
`\text{cos}(\theta)/(3)` [Identity used → cos²a - sin²a = cos(2a)]

Hence, left hand side of the given equation = Left hand side of the equation.