Question

cosec a+sina/coseca-sina=5/3​

Answer 1

Answer:

Given that p = 2sinA /1+cosA+sinA and q = cosA / 1+sinA We have to prove p+q = 1 Proof: LHS p+q=(2sinA/1+casA+sinA) + (casA/1+sinA) ={2sinA(1+sinA) + cosA(1+casA+sinA)} / (1+sinA+casA)(1+sinA) =(2sinA+2sinAsinA + casA+casAcasA+casAsinA) / (1+sinA+casA)(1+sinA) ={2sinA+2sinAsinA + casAcasA +casA(1+sinA)} / (1+sinA+casA)(1+sinA) ={2sinA+sinAsinA+1+casA(1+sinA) } / (1+sinA+casA)(1+sinA) ={sinAsinA +sinA+sinA+1 +casA(1+sinA)} / (1+sinA+casA)(1+sinA) ={sinAsinA+sinA +(sinA+1)(1+casA)} / (1+sinA+casA)(1+sinA) ={sinA(sinA+1) +(sinA+1)(casA+1)} / (1+sinA+casA)(1+sinA) ={(sinA+1)(sinA+casA+1)} / (1+sinA+casA)(1+sinA) =1 RHS Hence Proved