Question

(sin²30° + 4cot²45° − sec²60°) = ?
(a) 0
(b) $\frac{1}{4}$
(c) 4
(d) 1

Answer 1

(b) $\frac{1}{4}$

$$\begin{gathered} \left({\sin }^2{30}^{\mathrm{o}}+4{\cot }^2{45}^{\mathrm{o}}-{\sec }^2{60}^{\mathrm{o}}\right) \\ =\left[{\left(\frac{1}{2}\right)}^2+4\times {\left(1\right)}^2-{\left(2\right)}^2\right] \\ =\left(\frac{1}{4}+4-4\right)=\frac{1}{4} \end{gathered}$$