Question

If tan(A/2) = x, then the value of x is

Answer 1

This is your answer

Answer 2

Answer:

The right is = 1-Cos A/sin A

Step-by-step explanation:

use formula, we know that cos(2Ф)=cos²Ф-sin²Ф

⇒cos(2Ф)=(1-sin²Ф)-sin²Ф

⇒cos(2Ф)=1-2 sin²Ф

replacing Ф by A/2,we get:

⇒cos A=1-2 sin²(A/2)

⇒2 sin²(A/2)=1-cos A

⇒sin²(A/2)=(1-cos A)/2

⇒sin(A/2)=√(1-cos A)/2

Similarly ⇒ cos(A/2)=√(1+cos A)/2

Now , to find: tan(A/2)

=sin(A/2)÷cos(A/2)

=√(1-cos A)/2÷√(1+cos A)/2

=√(1-cos A/2×√2/(1+cos A)

=√1-cos A/1+cos a

=√1-cos A/1-cos² A=√(1-cos A)²/sin² A

=1-Cos A/sin A