Question

Prove that cosec A - cot A = sinA /1 + cos A

Answer 1

LHS = cosecA - cotA
        = 1/sinA - cosA/sinA
        = (1 - cosA)/sinA
on rationalising we get,
= (1 - cosA)/sinA * (1 + cosA)/(1 + cosA+
= sin^2A/sinA(1 + cosA)
= sinA/(1+ cosA) = RHS Hence Proved.  

Answer 2

cosec a-cot a
                       =1/sin a-cos a/sin a
                       =1-cos a/sin a
                        =multiply by sin a
                        =sin a(1-cos a)/sin2a
                         =sin a(1-cos a)/1-cos2a
                         =sin a(1-cos a)/(1+cos a)(1-cos a)
                         =sin a/1+cos a
hope this helps u
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