Question
Mon July 23, 2012 By: Chethan U

P.T 1/(CosecA-CotA )-1/SinA=1/SinA-1/(CosecA+CotA )

Expert Reply
Mon July 23, 2012
LHS = 1/(cosecA - cotA) - cosecA
= {(cosecA + cotA)/cosec²A - cot²} - cosecA

we know that cosec²A - cot²A = 1

= cosecA + cotA - cosecA

= cosecA - (cosecA - cotA)

= cosecA - (cosecA - cotA)(cosecA + cotA)/(cosecA + cotA)

= cosecA -(cosec²A - cot²A)/(cosecA + cotA)

= 1/sinA - 1/(cosecA + cotA)  
= RHS
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