Question

Find the values of the following
(i) 2 tan ^₂ 45$°$ + cos ^₂ 30 $-$ sin ^₂ 60$°$
(ii) 4cot ^₂ 45$°$ $-$ sec ^₂ 60$°$ + cosec ^₂ 30$°$+cot 90$°$

Answer 1

(i)
$$\begin{gathered} 2{\tan }^{2}45°+{\cos }^{2}30°-{\sin }^{2}60° \\ =2\times {\left(1\right)}^2+{\left(\frac{\sqrt{3}}{2}\right)}^2-{\left(\frac{\sqrt{3}}{2}\right)}^2 \\ =2+0 \\ =2 \end{gathered}$$

(ii)
$$\begin{gathered} 4{\cot }^{2}45°-{\sec }^{2}60°+{\mathrm{cosec}}^{2}30°+\cot 90° \\ =4\times {\left(1\right)}^2-{\left(2\right)}^2+{\left(2\right)}^2+0 \\ =4+0 \\ =4 \end{gathered}$$