#### RussianTank

##### New member

- Joined
- Nov 20, 2020

- Messages
- 3

How could I alternate between forms to show that:

√[2 + √(3)] / 2 = ( √2 + √2√3 ) / 4

The original problem was finding the exact value of cos(15).

The answer to the left I got using the half-angle formula, and answer to the right is through subtraction formula. Both are correct.

But how to alternate between these forms arithmetically?

If for example I start to convert the left to right by multiplying numerator and denominator by 2, I get:

2[√( 2 + √(3) )] / (2x2)

But now I am stuck. I need help from here.

Regards

√[2 + √(3)] / 2 = ( √2 + √2√3 ) / 4

The original problem was finding the exact value of cos(15).

The answer to the left I got using the half-angle formula, and answer to the right is through subtraction formula. Both are correct.

But how to alternate between these forms arithmetically?

If for example I start to convert the left to right by multiplying numerator and denominator by 2, I get:

2[√( 2 + √(3) )] / (2x2)

But now I am stuck. I need help from here.

Regards

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