Question

If tansquare=1/√5,then cosecsquareA - secsquareA / cosecsquare A + secsquare A is

Answer 1

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

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