Question

prove that: cotA + cosecA - 1/cotA - cosecA + 1 = 1 - cosA/sinA

Answer 1

(cosA/sinA)+(1/sinA)-1/cosA/sinA-1/sinA+1
=(cosA+1-sinA)/sinA÷(cosA-1+sinA)/sinA
=(cosA-sinA+1)/(cosA+sinA-1)
multiply and divide by (cosA-sinA+1)
(cosA-sina+1)(cosA-sinA+1)/(cosA+sinA-1)(cosA-sinA+1)
=(cos²A-sinAcosA+cosA-sinAcosA+sin²A-sinA+cosA-sinA+1)/(cos²a-sin²A-cosA+sinA-1)
(2+2cosA-2sinA-2sinAcosA)(cos2A-cosA+sinA-1)