Question

prove that cot A-cos A/cot A+cos A = cosec A-1/cosec A+1

Answer 1

Answer:

Step-by-step explanation:

(Cot A - CosA)/ (Cot A + Cos A) = (Cosec A - 1)/(Cosec A + 1)

L.H.S

[(CosA/SinA - CosA)] / [(CosA/SinA + CosA)]

[(CosA - CosASinA) / SinA] / [ (CosA + CosASinA) / SinA]

[CosA - CosASinA] / [CosA + CosASinA]

[CosA(1 - SinA] / CosA(1+Sin A) ] =

(1 - SinA)/ (1 + SinA)

R.H.S

(Cosec A - 1) / (Cosec A + 1)

= (1/SinA - 1) / ( 1/ SinA + 1)

= [ ( 1 - SinA)/Sin A ] / [ ( 1 + SinA) / SinA ]

= (1 - Sin A)/(1 + SinA)

Alternatively

L.H.S

(1 - Sin A)/ (1 + Sin A)

Divide each term by Sin A

(1/SinA - SinA/SinA) / (1/SinA + SinA/SinA) =

(Cosec A - 1) / (Cosec A + 1) = R.H.S

Cheers

Answer 2

Here is the ans. It may help u