What is the value of ³ 60^{} 30^{} - 2² 45^{} + 3 60^{} 45^{} - ² 60^{}?

Correct Answer is : −358-35/8−835

Correct Answer is : −358-35/8−835

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Trigonometry Practice Test 2

Question : 18 of 22

Marks: +1, -0

\sin^3 60^{\circ} \cot 30^{\circ} - 2\sec^2 45^{\circ}

+ 3\cos 60^{\circ} \tan 45^{\circ} - \tan^2 60^{\circ}

Solution:

Concept:

Substitute the standard trigonometric values for special angles and simplify.

Explanation:

Given expression:

\sin^3 60^\circ \cot 30^\circ - 2\sec^2 45^\circ + 3\cos 60^\circ \tan 45^\circ - \tan^2 60^\circ

Use values:

\sin 60^\circ=\frac{\sqrt{3}}{2}

\cot 30^\circ=\sqrt{3}

\sec 45^\circ=\sqrt{2}

\cos 60^\circ=\frac{1}{2}

\tan 45^\circ=1

\tan 60^\circ=\sqrt{3}

Substitute these values:

=\left(\frac{\sqrt{3}}{2}\right)^3(\sqrt{3}) - 2(\sqrt{2})^2 + 3\left(\frac{1}{2}\right)(1) - (\sqrt{3})^2

Simplify each term:

=\frac{9}{8}-4+\frac{3}{2}-3

=\frac{9}{8}+\frac{12}{8}-\frac{56}{8}

=-\frac{35}{8}

Answer:

The value is

-\frac{35}{8}

, which matches option B.

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