Evaluate - 2 - 3cos 300 4-sin 45- 4-3sin 2 60- 2 45-1 - 4 30

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Standard Values of Trigonometric Ratios

Evaluate : 2 ...

Question

Evaluate : 2/3(cos30^4-sin45^4)-3(sin²60-sec²45)+1/4cot²30

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Solution

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\frac{2}{3} ({cos}^{4} 30^{\circ} - {sin}^{4} 45^{\circ}) - 3 ({sin}^{2} 60^{\circ} - {sec}^{2} 45^{\circ}) + \frac{1}{4} {cot}^{2} 30^{\circ}

4 ({sin}^{4} 30^{\circ} + {cos}^{4} 60^{\circ}) - \frac{2}{3} ({sin}^{2} 60^{\circ} - {cos}^{2} 45^{\circ}) + \frac{1}{2} {tan}^{2} 60^{\circ}

(i) \frac{1 + {tan}^{2} 30^{\circ}}{1 - {tan}^{2} 30^{\circ}} + c o s e c^{2} 60^{\circ} - {cos}^{2} 45^{\circ} + {sin}^{2} 45^{\circ} + \frac{1 + {cot}^{2} 60^{\circ}}{1 - {cot}^{2} 60^{\circ}}

(i i) 4 ({sin}^{4} 30^{\circ} + {cos}^{4} 60^{\circ}) - 3 ({cos}^{2} 45^{\circ} - {sin}^{2} 90^{\circ})

\frac{2}{3} (\cos^{4} 30 ° - \sin^{4} 45 °) - 3 (\sin^{2} 60 ° - \sec^{2} 45 °) + \frac{1}{4} \cot^{2} 30 ° = ?

\frac{53}{12}

\frac{73}{24}

\frac{113}{24}

\frac{83}{12}

^{2} 45 - c o s^{2} 30 = x . c o s 45. s i n 45

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