Question

CosA -sinA+1
------------------- =cosecA+cotA
CosA+sinA-1

Answer 1

Step-by-step explanation:

taking from LHS

cos A-sinA +1 /cosA +sinA -1

dividing the whole equation by sinA it will be--

cotA-1+cosec A/ cot A+1-cosecA

or

cotA+cosecA -1 /cot A - cosec A +1

we know that--- 1=cosec^2A - cot^2 A

so..

cot A +cosecA -(cosec^2 A - cot^2A)/cotA -cosecA

(a^2-b^2)=(a-b) (a+b)

so..

cotA +cosec A-(cosecA -cotA)(cosecA +cotA )/cotA-cosecA +1

taking minus common

(cotA + cosecA)(1-cosecA+cotA)/ cotA -cosecA +1

=cotA+cosecA

hence LHS=RHS