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

$\frac{π}{2}$
$\frac{π}{3}$
$\frac{π}{4}$
$\frac{π}{5}$

The correct answer is: $straight pi over 4$

Related Questions to study

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

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

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

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

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

$Error converting from MathML to accessible text.$

$Error converting from MathML to accessible text.$

$text If end text x squared plus y squared plus z squared equals r squared$ and $tan space straight alpha equals xy over straight x comma tan space straight beta equals straight y over xs comma tan space straight gamma equals xe over straight y$ then $straight alpha plus straight beta plus straight gamma equals$

$text If end text x squared plus y squared plus z squared equals r squared$ and $tan space straight alpha equals xy over straight x comma tan space straight beta equals straight y over xs comma tan space straight gamma equals xe over straight y$ then $straight alpha plus straight beta plus straight gamma equals$

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

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

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$text In a end text straight triangle ABC text if end text tan text end text straight B equals fraction numerator 2 sin space Asin space straight C over denominator sin begin display style space end style left parenthesis straight A plus straight C right parenthesis end fraction text then end text tan space straight A comma tan space straight B comma tan space straight C text are in end text$

$text In a end text straight triangle ABC text if end text tan text end text straight B equals fraction numerator 2 sin space Asin space straight C over denominator sin begin display style space end style left parenthesis straight A plus straight C right parenthesis end fraction text then end text tan space straight A comma tan space straight B comma tan space straight C text are in end text$

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

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

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

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

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

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

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

$text If end text fraction numerator cos begin display style text end text end style A over denominator cos begin display style text end text end style B end fraction equals n text and end text fraction numerator sin begin display style text end text end style A over denominator sin begin display style text end text end style B end fraction equals m text then end text open parentheses m squared minus n squared close parentheses sin squared text end text B equals$

$text If end text fraction numerator cos begin display style text end text end style A over denominator cos begin display style text end text end style B end fraction equals n text and end text fraction numerator sin begin display style text end text end style A over denominator sin begin display style text end text end style B end fraction equals m text then end text open parentheses m squared minus n squared close parentheses sin squared text end text B equals$

Find the projection of the vector $a with rightwards arrow on top equals 2 i with hat on top plus 3 j with hat on top plus 2 k with hat on top$ on the vector $stack b with rightwards arrow on top equals$ $i with ˆ on top plus 2 j with ˆ on top plus k with ˆ on top.$

Find the projection of the vector $a with rightwards arrow on top equals 2 i with hat on top plus 3 j with hat on top plus 2 k with hat on top$ on the vector $stack b with rightwards arrow on top equals$ $i with ˆ on top plus 2 j with ˆ on top plus k with ˆ on top.$

Let $stack a with ‾ on top equals 2 stack i with ˆ on top plus 3 stack j with ˆ on top minus 6 stack k with ˆ on top comma stack b with rightwards arrow on top equals 2 stack i with ˆ on top minus 3 stack j with ˆ on top plus 6 stack k with ˆ on top$ and $stack c with ‾ on top equals negative 2 stack i with ˆ on top plus 3 stack j with ˆ on top plus 6 stack k with ˆ on top times$ let $stack a with rightwards arrow on top subscript 1 end subscript$ be projection of $stack a with rightwards arrow on top$ on $stack b with rightwards arrow on top$ and $stack a with rightwards arrow on top subscript 2 end subscript$ be the projection of $stack a with rightwards arrow on top subscript 1 end subscript$ on $stack c with rightwards arrow on top$ . Then $stack a with rightwards arrow on top subscript 2 end subscript equals$

Let $stack a with ‾ on top equals 2 stack i with ˆ on top plus 3 stack j with ˆ on top minus 6 stack k with ˆ on top comma stack b with rightwards arrow on top equals 2 stack i with ˆ on top minus 3 stack j with ˆ on top plus 6 stack k with ˆ on top$ and $stack c with ‾ on top equals negative 2 stack i with ˆ on top plus 3 stack j with ˆ on top plus 6 stack k with ˆ on top times$ let $stack a with rightwards arrow on top subscript 1 end subscript$ be projection of $stack a with rightwards arrow on top$ on $stack b with rightwards arrow on top$ and $stack a with rightwards arrow on top subscript 2 end subscript$ be the projection of $stack a with rightwards arrow on top subscript 1 end subscript$ on $stack c with rightwards arrow on top$ . Then $stack a with rightwards arrow on top subscript 2 end subscript equals$

parallel

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