cosA-sinA+1/cosA+sinA-1
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Step-by-step explanation:
L.H.S = cos A -sinA +1 /cosA +sinA -1
divide and multyply by sin A
= sinA (cosA-sinA +1) / sinA (cosA + sinA -1)
= sinAcosA - sin²A + sinA / sinA (cosA + sinA -1)
= sinAcosA +sinA -( 1 - cos²A) / sinA (cos A + sin A - 1 )
= sinA(cosA+1) - (1-cosA) (1+ cos A) / sinA ( cosA + sinA - 1)
= (1 + cos A) ( sinA + cos A -1 ) / sinA ( cosA +sinA -1 )
= 1 + cosA / sinA
= 1 / sinA + cosA / sinA
R.H.S = cosecA + cotA
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