If tansquare=1/√5,then cosecsquareA - secsquareA / cosecsquare A + secsquare A is
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Solution :
tan²A = 1/√5 ---( 1 )
(cosec² A - sec²A)/( cosec²A + sec²A )
Divide numerator and denominator
by sin²A , we get
= ( 1 - tan²A )/( 1 + tan²A )
= [ 1 - 1/√5 ]/[ 1 + 1/√5 ]
= ( √5 - 1 )/( √5 + 1 )
= ( √5 - 1 )²/[ ( √5 +1 )( √5 - 1 ) ]
= ( √5 - 1 )²/ [ (√5)² - 1² ]
= ( √5 - 1 )² /4
••••
tan²A = 1/√5 ---( 1 )
(cosec² A - sec²A)/( cosec²A + sec²A )
Divide numerator and denominator
by sin²A , we get
= ( 1 - tan²A )/( 1 + tan²A )
= [ 1 - 1/√5 ]/[ 1 + 1/√5 ]
= ( √5 - 1 )/( √5 + 1 )
= ( √5 - 1 )²/[ ( √5 +1 )( √5 - 1 ) ]
= ( √5 - 1 )²/ [ (√5)² - 1² ]
= ( √5 - 1 )² /4
••••
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