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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

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

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From the figure AOC=

From the figure AOC=

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

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