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Cos(A+B)Cos(A-B)

Calculate the...

Question

Calculate the value of the expression $4 ({sin}^{4} 30^{\circ} + {cos}^{4} 30^{\circ}) - 3 ({cos}^{2} 45^{\circ} - {sin}^{2} 90^{\circ})$

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Solution

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

= $4 ((\frac{1}{2})^{4} + (\frac{\sqrt{3}}{2})^{4}) - 3 ((\frac{1}{\sqrt{2}})^{2} - (1)^{2})$

= $4 (\frac{1}{16} + \frac{9}{16}) - 3 (\frac{1}{2} - 1)$

= $4 (\frac{10}{16}) + \frac{3}{2}$

= $\frac{5}{2} + \frac{3}{2}$
= $4$

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Similar questions

Q. The value of

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

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

Q. Evaluate each of the following :

4 (s i n^{4} 30^{\circ} + c o s^{2} 60^{\circ}) - 3 (c o s^{2} 45^{\circ} - s i n^{2} 90^{\circ}) - s i n^{2} 60^{\circ}

Q. The value of

4 ({sin}^{4} 30^{\circ} + c o s^{4} 60^{\circ}) ({cos}^{2} 45^{\circ} - {sin}^{2} 90^{\circ}) + {tan}^{4} 45^{\circ} - {cot}^{2} 45^{\circ}

Q. Evaluate the following

(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})

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Cos(A+B)Cos(A-B)

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