How do I know the following equation is true:

The equation is true

Step-by-step explanation:

The best way to check if this equate is true is to convert the pi in radians to degree and actually evaluate the trigonometric terms.

Mathematically we know that pi = 180 degrees

So pi/8 = 22.5

and pi/4 = 180/4 = 45

So let’s make our check.

Insert pi = 22.5 and pi = 45

So we have;

tan 22/5 = √(1-cos45)/(1+cos45)

Now let’s evaluate this using a calculator.

tan 22/5 = 0.414213562373

The term in the root; 0.171572875254

The square root of this number is 0.414213562373

This is exactly as what is obtained with the tan 22.5

So we conclude that what we have is true

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