The value of cos4 -4-cos4 -6 - sin4 -6- sin4 4 -3 is

The correct option is D 23/16 nbsp; cos ^ 4 π nbsp;/ 4 + cos ^ 4 π nbsp;/ 6 + sin ^ 4 π nbsp;/ 6 + sin ^ 4 4π nbsp;/ 3 = cos ^ 4 ...

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Standard X

Mathematics

Complementary Trigonometric Ratios

The value of ...

Question

The value of $c o s^{4} \frac{π}{4} + c o s^{4} \frac{π}{6} + s i n^{4} \frac{π}{6} + s i n^{4} \frac{4 π}{3}$ is

\frac{1}{16}

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\frac{1}{8}

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\frac{5}{16}

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\frac{23}{16}

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Solution

The correct option is D $\frac{23}{16}$
${c o s}^{4} \frac{π}{4} + {c o s}^{4} \frac{π}{6} + {s i n}^{4} \frac{π}{6} + {s i n}^{4} \frac{4 π}{3} = {c o s}^{4} 45^{\circ} + {c o s}^{4} 30^{\circ} + {s i n}^{4} 30^{\circ} + {s i n}^{4} 240^{\circ} = {(\frac{1}{\sqrt{2}})}^{4} + {(\frac{\sqrt{3}}{2})}^{4} + {(\frac{1}{2})}^{4} + {(s i n (180^{o} + 60^{\circ}))}^{4} = \frac{1}{4} + \frac{9}{16} + \frac{1}{16} + {(- s i n 60^{\circ})}^{4} = \frac{1}{4} + \frac{9}{16} + \frac{1}{16} + {(- \frac{\sqrt{3}}{2})}^{4} = \frac{1}{4} + \frac{9}{16} + \frac{1}{16} + \frac{9}{16} = \frac{1}{4} + \frac{19}{16} = \frac{23}{16} (A n s)$ .

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Similar questions

Q. The value of

{cos}^{4} \frac{π}{4} - {cos}^{4} \frac{π}{6} + {sin}^{4} \frac{π}{6} + {sin}^{4} \frac{4 π}{3}

Q. The value of

{cos}^{2} (\frac{π}{4}) + {cos}^{4} (\frac{π}{6}) + {sin}^{4} (\frac{π}{3})

Q. The principal value of

{sin}^{- 1} (sin \frac{4 π}{3}) + {cos}^{- 1} (cos \frac{4 π}{3})

Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

Q. The value of

{sin}^{4} \frac{π}{16} + {sin}^{4} \frac{3 π}{16} + {sin}^{4} \frac{5 π}{16} + {sin}^{4} \frac{7 π}{16}

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The value of cos4π4+cos4π6+sin4π6+sin44π3 is

The correct option is D 2316cos4π4+cos4π6+sin4π6+sin44π3=cos445∘+cos430∘+sin430∘+sin4240∘=(1√2)4+(√32)4+(12)4+(sin(180o+60∘))4=14+916+116+(−sin60∘)4=14+916+116+(−√32)4=14+916+116+916=14+1916=2316(Ans).

The value of $c o s^{4} \frac{π}{4} + c o s^{4} \frac{π}{6} + s i n^{4} \frac{π}{6} + s i n^{4} \frac{4 π}{3}$ is