Question

Prove that Cos A upon 1 minus tan a + sin square A upon Sin A minus Cos A is equal to Sin A + Cos A

Answer 1

Solution

LHS (cosA /1-tanA)+(sin^2A/sinA-cosA)

(cosA/1-sinA/cosA)+(sin^2A/sinA-cosA)

(cosA/cosA-sinA/cosA)+(sin^2A/sinA-cosA)

(cos^2A/cosA-sinA)+(sin^2A/sinA-cosA)

(cos^2A/cosA-sinA)-(sin^2A/cosA-sinA) (multiply sin^2A&sinA-cosA by -1)

cos^2A-sin^2A/cosA-sinA

(cosA-sinA)(cosA+sinA)/cosA-sinA)

cosA+sinA

RHS cosA+sinA

LHS=RHS

Hence proved