Question

prove that cos theta upon 1 minus tan theta -sin square theta upon sin theta minus cos theta = sin theta + cos theta

Answer 1

take LHS 
cosA- sin A+1/ cosA +sinA -1
now dividing numerator and denominator by sinA 
=> cosecA +cotA-1 / cotA - cosecA +1
=> cosecA +cotA -(cosecA^2 - cotA^2) / cotA- cosecA+1
=> cosecA + cotA - ( cosecA+cotA) (cosecA-cotA) / cotA - cosecA+1
=> (cosecA+ cotA)(cot A-cosecA+1) / cotA- cosecA +1
=> cosecA +cotA
=>RHS
HENCE,PROVED!