1 by cosec a minus cot a minus 1 by sin a is equal to 1 by Sin A minus 1 by cosec A + cot a
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LHS = 1/cosec A - cot A - 1/ sin A
= 1/cosec A cot A * cosec A + cot A/ cosec A + cot A 1/sin A
= (cosec A + cot A)/(cosec^2A -
cot^2A) - 1/sin A
= (cosec A + cot A)/(cosec^2A - cot^2A) - cosec A
= cosec A + cot A - cosec A
= cot A.
RHS = 1/sin A - 1/cosecA+cotA
= cosecA - (cosecA - cotA)/ (cosec^2A - cot^2A)
= cosec A - (cosec A-cot A)
= cosec A - cosec A + cot A
= cot A.
LHS = RHS.
Hope this helps!
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