prove that 1/(cosec theta - cot theta) - 1/sin theta = 1/sin theta -1/(cosec theta + cot theta)
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Trigonometry
LHS = {1/( cosecA - cotA)} -1/sin A
= {(cosec²A-cot²A)/(cosecA-cotA)} - 1/sinA
= (cosecA + cotA) - cosecA
= cosecA - ( cotA - cosecA)
= (1/sinA) - {( cotA - cosecA)/(cosec²A - cot²A)}
= (1/sinA) - 1/(cosecA + cotA)
That's it
Hope it helped
(O_o)
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