Question

(1-costhita+sinthita)(1+costhita+sinthita)=2sinthita(1+sinthita)

Answer 1

LHS = (1+cosϴ+sinϴ) (1-cosϴ+sinϴ)
(1+sinϴ)^2-(cosϴ)^2
1+sin^2ϴ+2sinϴ-cos^2ϴ
1+sin^2ϴ+2sinϴ-1+sin^2ϴ
2sinϴ+2sin^2ϴ
2sinϴ(1+sinϴ) = RHS

LHS=RHS
Hence,proved