P.T 1/(CosecA-CotA )-1/SinA=1/SinA-1/(CosecA+CotA )
Asked by chethan U | 23rd Jul, 2012, 07:11: PM
Expert Answer:
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
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
Answered by | 23rd Jul, 2012, 10:16: PM
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