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Question

$text If end text tan text end text straight A equals 17 over 18 comma tan space straight B equals 1 over 35 text then end text cos text end text left parenthesis straight A plus straight B right parenthesis equals$

1
$\sqrt{2}$
-1
$\frac{1}{\sqrt{2}}$

The correct answer is: $fraction numerator 1 over denominator square root of 2 end fraction$

$table attributes columnspacing 1em end attributes row cell cos space left parenthesis straight A plus straight B right parenthesis equals fraction numerator 18 over denominator square root of 613 end fraction fraction numerator 35 over denominator square root of 2 square root of 613 end fraction minus fraction numerator 17 over denominator square root of 613 square root of 2 square root of 613 end fraction end cell row cell equals fraction numerator 613 over denominator left parenthesis 613 right parenthesis square root of 2 end fraction equals square root of square root of 2 end root end cell end table$

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$text If end text straight A comma straight B text are acute angles, end text sin space straight A equals 4 over 5 comma tan invisible function application straight B equals 5 over 12 text then end text sin text end text left parenthesis straight A plus straight B right parenthesis equals$

$text If end text straight A comma straight B text are acute angles, end text sin space straight A equals 4 over 5 comma tan invisible function application straight B equals 5 over 12 text then end text sin text end text left parenthesis straight A plus straight B right parenthesis equals$

$text In a end text straight triangle ABC comma straight A text is obtuse, end text sin invisible function application straight A equals 3 over 5 comma sin space straight B equals 5 over 13$ then sin c=

$text In a end text straight triangle ABC comma straight A text is obtuse, end text sin invisible function application straight A equals 3 over 5 comma sin space straight B equals 5 over 13$ then sin c=

$text If end text sin text end text straight A equals fraction numerator 1 over denominator square root of 2 straight pi end root end fraction comma sin space straight B equals fraction numerator 1 over denominator square root of 5 end fraction comma 0 less than straight A comma straight B less than straight pi over 4 text then end text straight A plus straight B equals$

$text If end text sin text end text straight A equals fraction numerator 1 over denominator square root of 2 straight pi end root end fraction comma sin space straight B equals fraction numerator 1 over denominator square root of 5 end fraction comma 0 less than straight A comma straight B less than straight pi over 4 text then end text straight A plus straight B equals$

parallel

$text If end text tan text end text straight A equals fraction numerator sin begin display style space end style straight B over denominator 1 minus xcos space straight B end fraction text and end text tan text end text straight B equals fraction numerator ysin space straight A over denominator 1 minus ycos space straight A end fraction text then end text fraction numerator sin begin display style text end text end style straight A over denominator sin begin display style text end text end style straight B end fraction equals$

$text If end text tan text end text straight A equals fraction numerator sin begin display style space end style straight B over denominator 1 minus xcos space straight B end fraction text and end text tan text end text straight B equals fraction numerator ysin space straight A over denominator 1 minus ycos space straight A end fraction text then end text fraction numerator sin begin display style text end text end style straight A over denominator sin begin display style text end text end style straight B end fraction equals$

$fraction numerator cos space x over denominator cos space left parenthesis x minus 2 y right parenthesis end fraction equals lambda not stretchy rightwards double arrow tan space left parenthesis x minus y right parenthesis tan space y equals$

$fraction numerator cos space x over denominator cos space left parenthesis x minus 2 y right parenthesis end fraction equals lambda not stretchy rightwards double arrow tan space left parenthesis x minus y right parenthesis tan space y equals$

In a $ΔABC$ , if $cos space Acos space Bcos space straight C equals 1 divided by 3$ , then the value of tan A tan B +tan B tan C +tan C tan A is

In a $ΔABC$ , if $cos space Acos space Bcos space straight C equals 1 divided by 3$ , then the value of tan A tan B +tan B tan C +tan C tan A is

parallel

$Error converting from MathML to accessible text.$

$Error converting from MathML to accessible text.$

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$text If end text straight A plus straight B plus straight C equals straight pi over 2 text then end text sum fraction numerator cos begin display style text end text end style left parenthesis straight B plus straight C right parenthesis over denominator cos begin display style text end text end style Bcos space straight C end fraction equals$

$text If end text straight A plus straight B plus straight C equals straight pi over 2 text then end text sum fraction numerator cos begin display style text end text end style left parenthesis straight B plus straight C right parenthesis over denominator cos begin display style text end text end style Bcos space straight C end fraction equals$

parallel

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in a $straight triangle P Q R comma open square brackets straight real numbers equals pi over 2 text if end text tan text end text open parentheses P over 2 close parentheses close$ and $tan space open parentheses straight Q over 2 close parentheses$ are the roots of the equation $a x squared plus b x plus c equals 0 left parenthesis a not equal to 0 right parenthesis$ then

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The value of $sin open parentheses a over 2 close parentheses open curly brackets 1 half plus sum from k equals 1 to n of cos left parenthesis k a right parenthesis close curly brackets$ is equal to

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parallel

The equation $2 sin x over 2 cos squared x minus 2 sin x over 2 sin squared x equals cos squared x minus sin squared x$ has a root for which the false statement is

The equation $2 sin x over 2 cos squared x minus 2 sin x over 2 sin squared x equals cos squared x minus sin squared x$ has a root for which the false statement is

If $0 less than theta comma ϕ less than pi divided by 2 text and end text x equals sum from n equals 0 to straight infinity of sin to the power of 2 n end exponent invisible function application theta comma y equals sum from n equals 0 to straight infinity of cos to the power of 2 n end exponent invisible function application ϕ subscript text and end text end subscript straight z equals sum from n equals 0 to straight infinity of cos to the power of straight n invisible function application left parenthesis theta plus ϕ right parenthesis cos to the power of straight n invisible function application left parenthesis theta minus ϕ right parenthesis$ then

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if $2 tan space A plus c o t space A equals tan space B$ then $c o t space A plus 2 tan space left parenthesis A minus B right parenthesis equals$

if $2 tan space A plus c o t space A equals tan space B$ then $c o t space A plus 2 tan space left parenthesis A minus B right parenthesis equals$

parallel

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