The value of 4cos2-3 - 2-6 - sin2-4 is

The correct option is D 116 4cos^2 π3+sec^2 π6 sin^2 π4=4×14+43 12=1+43 12=6+8 36=116 ...

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Byju's Answer

Standard XII

Mathematics

Circular Measurement of Angle

The value of ...

Question

The value of $4 {cos}^{2} \frac{π}{3} + {sec}^{2} \frac{π}{6} - {sin}^{2} \frac{π}{4}$ is

\frac{13}{6}

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\frac{11}{6}

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\frac{7}{6}

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\frac{5}{6}

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Solution

The correct option is D $\frac{11}{6}$
$4 {cos}^{2} \frac{π}{3} + {sec}^{2} \frac{π}{6} - {sin}^{2} \frac{π}{4} = 4 \times \frac{1}{4} + \frac{4}{3} - \frac{1}{2} = 1 + \frac{4}{3} - \frac{1}{2} = \frac{6 + 8 - 3}{6} = \frac{11}{6}$

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Similar questions

Q. The value of

{sin}^{2} \frac{π}{6} + {cos}^{2} \frac{π}{3} - {tan}^{2} \frac{π}{4} + {cot}^{2} \frac{π}{2}

is equal to

Q. Question 6
Explain why

7 \times 11 \times 13 + 13

and

7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5

are composite numbers.

Q. Calculate the values of the determinants:

∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} 7 & 13 & 10 & 6 5 & 9 & 7 & 4 8 & 12 & 11 & 7 4 & 10 & 6 & 3 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣

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. Find

(\frac{3}{11} \times \frac{5}{6}) - (\frac{9}{12} \times \frac{4}{3}) + (\frac{5}{13} \times \frac{6}{15})

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The value of 4cos2π3+sec2π6−sin2π4 is

The correct option is D 1164cos2π3+sec2π6−sin2π4=4×14+43−12=1+43−12=6+8−36=116

The value of $4 {cos}^{2} \frac{π}{3} + {sec}^{2} \frac{π}{6} - {sin}^{2} \frac{π}{4}$ is

The correct option is D $\frac{11}{6}$
$4 {cos}^{2} \frac{π}{3} + {sec}^{2} \frac{π}{6} - {sin}^{2} \frac{π}{4} = 4 \times \frac{1}{4} + \frac{4}{3} - \frac{1}{2} = 1 + \frac{4}{3} - \frac{1}{2} = \frac{6 + 8 - 3}{6} = \frac{11}{6}$