Question

please solve this problem friends

Answer 1

Here,
RHS=cosecA+cotA

LHS=(cosA-sinA+1)/(cosA+sinA-1)

LHS=(cosA-sinA+1)/(cosA+sinA-1)×(cosA-sinA+1)/(cosA-sinA+1)

LHS=(cos²A-cosAsinA+cosA-cosAsinA+sin²A-sinA+cosA-sinA+1)/(cos²A-cosAsinA+cosA+cosAsinA-sin²A+sinA-cosA+sinA-1)


LHS=(2-2sinAcosA+2cosA-2sinA)/(cos²A-sin²A+2sinA-1)

LHS=2(1-sinAcosA+cosA-sinA)/(1-sin²A-sin²A+2sinA-1)

LHS=2{(1-sinA)+cosA(1-sinA)}/(2sinA-2sin²A)

LHS=2(1-sinA)(1+cosA)/{2sinA(1-sinA)}

LHS{(1+cosA)/sinA

LHS=1/sinA+cosA/sinA

LHS=cosecA+cotA

LHS=RHS

Hence proved.