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Question

$text If end text x squared plus y squared plus z squared equals r squared$ 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 $straight alpha plus straight beta plus straight gamma equals$

$\frac{π}{4}$
$π$
$π / 2$
$π / 3$

The correct answer is: $pi divided by 2$

Related Questions to study

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

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

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

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

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

parallel

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

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

parallel

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

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

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

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 $stack b with rightwards arrow on top equals$ $i with ˆ on top plus 2 j with ˆ on top plus k with ˆ on top.$

parallel

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 $stack a with rightwards arrow on top subscript 2 end subscript equals$

$text If end text sin text end text A plus sin space B equals square root of 3 left parenthesis cos space B minus cos space A right parenthesis$ then $sin space 3 A plus sin space 3 B equals$

$text If end text sin text end text A plus sin space B equals square root of 3 left parenthesis cos space B minus cos space A right parenthesis$ then $sin space 3 A plus sin space 3 B equals$

$s i n squared space alpha plus c o s squared space left parenthesis alpha plus beta right parenthesis plus 2 s i n space alpha s i n space beta c o s space left parenthesis alpha plus beta right parenthesis equals$

$s i n squared space alpha plus c o s squared space left parenthesis alpha plus beta right parenthesis plus 2 s i n space alpha s i n space beta c o s space left parenthesis alpha plus beta right parenthesis equals$

parallel

$text If end text sin text end text x cos space y equals 1 fourth$ and $3 tan space x equals 4 tan space y$ then $sin space left parenthesis x minus y right parenthesis equals$

$text If end text sin text end text x cos space y equals 1 fourth$ and $3 tan space x equals 4 tan space y$ then $sin space left parenthesis x minus y right parenthesis equals$

$c o t space A c o t space B equals 2 comma cos space left parenthesis A plus B right parenthesis equals 3 divided by 5 rightwards double arrow sin space A sin space B equals$

$c o t space A c o t space B equals 2 comma cos space left parenthesis A plus B right parenthesis equals 3 divided by 5 rightwards double arrow sin space A sin space B equals$

$text If end text x cos space theta equals y cos space open parentheses theta plus fraction numerator 2 pi over denominator 3 end fraction close parentheses equals z cos space open parentheses theta plus fraction numerator 4 pi over denominator 3 end fraction close parentheses$ then the value of $1 over x plus 1 over y plus 1 over z equals$

$text If end text x cos space theta equals y cos space open parentheses theta plus fraction numerator 2 pi over denominator 3 end fraction close parentheses equals z cos space open parentheses theta plus fraction numerator 4 pi over denominator 3 end fraction close parentheses$ then the value of $1 over x plus 1 over y plus 1 over z equals$

parallel

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