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ScanSolve AI Tutor · Accepted Answer

Here is the solution for question 9(ii):

Substitute the known values of the trigonometric ratios.
We know that:
$\sin 30^\circ = \frac{1}{2}$
$\tan 60^\circ = \sqrt{3}$
$\cos 60^\circ = \frac{1}{2}$
$\sec 30^\circ = \frac{2}{\sqrt{3}}$
Substitute these values into the given expression.
$2 \sin^2 30^\circ \tan 60^\circ - 3 \cos^2 60^\circ \sec^2 30^\circ$ $= 2 \left(\frac{1}{2}\right)^2 (\sqrt{3}) - 3 \left(\frac{1}{2}\right)^2 \left(\frac{2}{\sqrt{3}}\right)^2$
Perform the squaring operations.
$= 2 \left(\frac{1}{4}\right) (\sqrt{3}) - 3 \left(\frac{1}{4}\right) \left(\frac{4}{3}\right)$
Multiply the terms in each part of the expression.
$= \frac{2\sqrt{3}}{4} - \frac{3 \times 1 \times 4}{4 \times 3}$ $= \frac{\sqrt{3}}{2} - \frac{12}{12}$ $= \frac{\sqrt{3}}{2} - 1$
Combine the terms to get the final answer.
$= \boxed{\frac{\sqrt{3}}{2} - 1}$

Answer