given: cosec a = 2 and `pi/2 < a < pi`

cosec is inverse of sine, thus

csc a = 1/sin a = 2

or, sin a = 1/2

cos a = `sqrt (1-sin^2 a) = sqrt(1-(1/2)^2) = sqrt (1-1/4) = sqrt (3/4) = - sqrt 3/2`

and tan a = `sina /cosa = (1/2)/(-sqrt3/2) = -1/sqrt3`

we chose negative signs for cos and tan, since a is between pi/2 and pi, and between these ranges, cos a and tan a will be negative.

Hope this helps.

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