Question

given coseca + cota =p. prove that sina= 2p÷p^2+1​

Answer 1

Given → cosecA+ cotA = p

R.T.P. → sinA = 2p/(p²+1)

Proof → we know that, cot²A+1 = cosec²A

Cosec²A - cot²A = 1

( cosecA- cotA) ( cosecA + cotA ) = 1

( CosecA-cotA) p = 1

( CosecA-cotA) =1/p -------> 1)

CosecA + cotA = p. (given) -----2)

Adding 1) and 2)

2 CosecA = 1/p +p = (p²+1)/p

CosecA = (p²+1)/2p

Using , sinA = 1/ CosecA

We get , sinA = 2p/(p²+1)