Question

The value of cos² 60° − 2 sin³ 30° + 3 cot⁴ 45° is ______.

Options

• 1

• −2

• 3

• 2

Answer 1

The value of cos² 60° − 2 sin³ 30° + 3 cot⁴ 45° is 3.

Explanation:

Substituting the exact trigonometric values: \[\cos 60^\circ = \frac{1}{2}\], \[\sin 30^\circ = \frac{1}{2}\], and cot 45° = 1.

\[\left(\frac{1}{2}\right)^2 - 2\left(\frac{1}{2}\right)^3 + 3(1)^4 = \frac{1}{4} - 2\left(\frac{1}{8}\right) + 3 = \frac{1}{4} - \frac{1}{4} + 3 = 3\]