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Class 10 > Learn Mathematics > If cosec |=3x and cot |=3/x. then find the value of...
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If cosec |=3x and cot |=3/x. then find the value of (x2-1/x2)

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CSAT Tutor, BPSC DI Tutor (Ex. Drishti IAS Senior Content Writer)

=1/9 use formula cosec² x -cot² x =1
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cosecβ = = 3X and cotβ = 3/X , to find value ( X2 - 1/X2 ) . we know , cosec2β = cot2β +1 putting value , (3X )2 = ( 3/X )2 +1 , OR 9X2 = 9 /X2 + 1 , OR 9X2 – 9/X2 = 1, OR 9( X2 - 1/X2 ) = 1, SO (X2 – 1/X2 ) = 1/9
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cosecβ = = 3X  and  cotβ =  3/X    , to find value   (  X2 - 1/X2 ) .    we know  , cosec2β  = cot2β  +1     putting value  ,    (3X )2 = ( 3/X )2 +1   ,

OR  9X2  =  9 /X2  + 1  ,     OR   9X2 – 9/X2  =  1,   OR   9( X2 -  1/X2 )  = 1,  SO     (X2 – 1/X2 )  =  1/9  

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Chemistry Teacher

Cosec^2A = 1 + cot^2 A (3x)^2 - 1/(3x)^2 = 1 9{(x)^2 - 1/(x)^2 = 1/(9) ans
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x=cosec/3
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cosec(^2)l=9x(^2). cot(^2)l=9/(x^2). Use cosec(^2)l-cot(^2)l=1. Then x^2-1/x^2=1/9
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WE take angle ,L = β , so cosecβ = = 3X and cotβ = 3/X , to find value ( X2 - 1/X2 ) . we know , cosec2β = cot2β +1 OR putting value , (3X )2 = ( 3/X )2 +1 , OR 9X2 = 9 /X2 + 1 , OR 9X2 – 9/X2 = 1, OR 9( X2 - 1/X2...
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WE  take  angle ,L  = β  ,    so       cosecβ = = 3X  and  cotβ =  3/X    , to find value   (  X2 - 1/X2 ) .    we know  , cosec2β  = cot2β  +1     OR   putting value  ,    (3X )2 = ( 3/X )2 +1   ,

OR  9X2  =  9 /X2  + 1  ,     OR   9X2 – 9/X2  =  1,   OR   9( X2 -  1/X2 )  = 1,  SO     (X2 – 1/X2 )  =  1/9   Answer

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Eco, Maths and Stats Tutor

cosec(^2)l=9x(^2). cot(^2)l=9/(x^2). Use cosec(^2)l-cot(^2)l=1. Then x^2-1/x^2=1/9
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Squaring the given equations, cosec(^2)l=9x(^2), cot(^2)l=9/(x^2).As we know cosec(^2)l-cot(^2)l=1 it gives 9x(^2)-9/(x^2)=1 which on simplification gives x^2-1/x^2=1/9
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