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Maths-

General

Easy

Question

If A,B,C re in A.P and $B equals pi over 4$ then $tan space A tan space B tan C$ =

1
2
3
4

The correct answer is: 1

$G i v e n comma B equals pi over 4 A comma B comma C space a r e space i n space A. P space therefore 2 B equals A plus C T o space f i n d comma tan space A tan space B tan C H e r e comma 2 B equals A plus C 2 open parentheses straight pi over 4 close parentheses equals A plus C open parentheses straight pi over 2 close parentheses equals A plus C A equals open parentheses straight pi over 2 close parentheses minus C A p p l y i n g space tan g e n t space o n space b o t h space t h e space s i d e s comma tan A equals tan open parentheses open parentheses straight pi over 2 close parentheses minus C close parentheses tan A equals c o t C tan A equals fraction numerator 1 over denominator tan C end fraction tan A tan C equals 1 space space space space space space space space space......... open parentheses 1 close parentheses N o w comma tan B equals tan open parentheses straight pi over 4 close parentheses tan B equals 1 space space space space space space space space.......... open parentheses 2 close parentheses F r o m space e q n space open parentheses 1 close parentheses space a n d space open parentheses 2 close parentheses comma tan A tan B tan C equals 1 cross times 1 equals 1$

Related Questions to study

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If $alpha comma beta comma gamma$ do not differ by a multiple of $straight pi$ and if $fraction numerator cos space left parenthesis alpha plus theta right parenthesis over denominator sin space left parenthesis beta plus gamma right parenthesis end fraction equals fraction numerator cos begin display style space end style left parenthesis beta plus theta right parenthesis over denominator sin begin display style space end style left parenthesis gamma plus alpha right parenthesis end fraction equals fraction numerator cos begin display style space end style left parenthesis gamma plus theta right parenthesis over denominator sin begin display style space end style left parenthesis alpha plus beta right parenthesis end fraction equals k$ Then k equals

From the figure AOC=

From the figure AOC=

In $capital delta$ ABC, D,E,F are the midpoints of sides BC, CA and AB respectively then ar $open parentheses B D E F close parentheses equals$

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chemistry-General

If $tan space open parentheses x plus pi over 4 close parentheses equals a$ then $sec squared space x$ =

If $tan space open parentheses x plus pi over 4 close parentheses equals a$ then $sec squared space x$ =

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Element $M plus N subscript 2 rightwards arrow with ΔH subscript 2 straight O on top NH subscript 3$ Element M belonging to group 13 can be

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In the given figure, ABCD is a Parallelogram then ar ( $capital delta$ AFB) is

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In the given fig. if C is the centre of Circle PQC = 25° and PRC =15° then QCR = i

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parallel

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