Question

Solve the given trigonometric equation:

what cotA+cosecA equal to ?

Answer 1

Given : cot A + Cosec A 

So As we know cot A = cos A/Sin A

And,

Cosec A = 1/Sin A

Therefore,now we have

 

Cot A + Cosec A = (Cos A/SinA) + (1/Sin A)

On solving it we will get

= (Cos A + 1)/Sin A

On solving the above equation using the half-angle formulas, we get

[Note: Cos A = 2 cos2 (A/2) – 1 and sin A = 2 Sin (A/2) Cos (A/2)]

Cot A + Cosec A = Cos (A/2) / Sin (A/2)

= Cot (A/2)

Hence, the value of cot A + Cosec A = Cot (A/2).

 

 

The value of cot A + Cosec A = Cot (A/2).