3 years ago

6 sin _ _ 3 csc _ = 0

1 answer:

6 0

6 sin θ - 3 csc θ = 0
6 sin θ = 3 csc θ = 3/sin θ
6 sin^2 θ = 3
sin^2 θ = 3/6 = 1/2
sin θ = sqrt(1/2)
θ = arcsin(sqrt(1/2)) = 45 degrees.
θ = 45°

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Answer:

1.U={1,2,3,4,5}

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Step-by-step explanation:

We are given that $A\cap (B\cup C)$ and $A\cup (B\cap C)$

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1.We have to construct a universe set U and non empty sets A,B and C so that above set in fact the same

Suppose U={1,2,3,4,5}

A={2}

B={2,3}

C={4,5}

$B\cap C=\phi$

$B\cup C=$ {2,3,4,5}

$A\cap (B\cup C)$ ={2} $\cap$ {2,3,4,5}={2}

$A\cup (B\cap C)$ ={2} $\cup\phi$ ={2}

Hence, $A\cap (B\cup C)=A\cup (B\cap C)$

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Suppose U={1,2,3,4}

A={1,2}

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$B\cap C=\phi$

$B\cup C$ ={2,3,4}

$A\cup (B\cap C)$ ={1,2} $\cup \phi$ ={1,2}

$A\cap (B\cup C)$ ={1,2} $\cap$ {2,3,4}={2}

Hence, $A\cap (B\cup C)\neq A\cup (B\cap C)$

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