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Question

The maximum value of $open parentheses c o s invisible function application alpha subscript 1 end subscript close parentheses open parentheses c o s invisible function application alpha subscript 2 end subscript close parentheses$ $open parentheses c o s invisible function application alpha subscript n end subscript close parentheses$ , under the restrictions $0 less or equal than alpha subscript 1 end subscript comma alpha subscript 2 end subscript comma horizontal ellipsis. alpha subscript n end subscript less or equal than fraction numerator pi over denominator 2 end fraction$ and $open parentheses c o t invisible function application alpha subscript 1 end subscript close parentheses open parentheses c o t invisible function application alpha subscript 2 end subscript close parentheses horizontal ellipsis open parentheses c o t invisible function application alpha subscript n end subscript close parentheses equals 1$

$\frac{1}{2^{n / 2}}$
$\frac{1}{2^{n}}$
$\frac{1}{2 n}$
1

The correct answer is: $fraction numerator text 1 end text over denominator 2 to the power of n divided by 2 end exponent end fraction$

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The maximum value of $s i n invisible function application left parenthesis c o s invisible function application x right parenthesis$ is equal to

The maximum value of $s i n invisible function application left parenthesis c o s invisible function application x right parenthesis$ is equal to

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The maximum value of $16 c o s to the power of 5 end exponent invisible function application theta minus 20 c o s to the power of 3 end exponent invisible function application theta plus 5 c o s invisible function application theta$ is

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$A equals s i n to the power of 8 end exponent invisible function application theta plus c o s to the power of 14 end exponent invisible function application theta$ then for all values of $theta$

$A equals s i n to the power of 8 end exponent invisible function application theta plus c o s to the power of 14 end exponent invisible function application theta$ then for all values of $theta$

Period of $s i n invisible function application left parenthesis x plus 2 x plus 3 x plus midline horizontal ellipsis plus n x right parenthesis$ is

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The function $f colon R rightwards arrow R g colon R rightwards arrow R$ are defined as follows $f left parenthesis x right parenthesis equals 0 left parenthesis x$ is rational $right parenthesis comma g left parenthesis x right parenthesis equals negative 1 left parenthesis x$ is rational $right parenthesis equals$ $1 left parenthesis x$ is irrational $equals 0$ ( $x$ is irrational $right parenthesis$ then fog $left parenthesis pi right parenthesis plus g o f invisible function application left parenthesis e right parenthesis$

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I) $f open parentheses fraction numerator p over denominator q end fraction close parentheses$ is real for each $fraction numerator p over denominator q end fraction element of Q$
II) $f open parentheses fraction numerator p over denominator q end fraction close parentheses$ is a complex number for each $fraction numerator p over denominator q end fraction element of Q$ Which of the following is correct?

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If $Z rightwards arrow Z$ is defined byf $left parenthesis x right parenthesis equals open curly brackets table row cell fraction numerator x over denominator 2 end fraction text if end text x text is even end text end cell row cell 0 text if end text x text odd end text end cell end table close$ then $f$ is

parallel

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If $f left parenthesis x right parenthesis equals l o g invisible function application open parentheses fraction numerator 1 plus x over denominator 1 minus x end fraction close parentheses$ then $f open parentheses x subscript 1 end subscript close parentheses plus f open parentheses x subscript 2 end subscript close parentheses equals$

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parallel

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