Question

The value of$4({\cos }^{2}60°{\cos }^{2}45°-\sin 30°)$ is

• A. $\frac{3}{2}$
• B. $\frac{-3}{2}$
• C. $-2$
• D. None of these

Answer 1

The correct option is B

$\frac{-3}{2}$

Find the value of$4({\cos }^{2}60°{\cos }^{2}45°-\sin 30°)$

We know $\cos 60°=\frac{1}{2},\cos 45°=\frac{1}{\sqrt{2}},\sin 30°=\frac{1}{2}$

$\begin{array}{rcl}4({\cos }^{2}60°{\cos }^{2}45°-\sin 30°)& =& 4\left[{\left(\frac{1}{2}\right)}^2.{\left(\frac{1}{\sqrt{2}}\right)}^2-\frac{1}{2}\right]\\ & =& 4\left[\frac{1}{4}.\frac{1}{2}-\frac{1}{2}\right]\\ & =& 4\left[\frac{1}{8}-\frac{1}{2}\right]\\ & =& 4\left[\frac{1-4}{8}\right]\left[\because \mathrm{LCM}\mathrm{of}8,2=8\right]\\ & =& \frac{4\times \left(-3\right)}{8}\\ & =& \frac{-3}{2}\\ \therefore 4({\cos }^{2}60°{\cos }^{2}45°-\sin 30°)& =& \frac{-3}{2}\end{array}$

$\therefore$The correct option is B.