Double and half argument

1.Write formulas for double and half arguments:

Formulas:
sin 2x = 2x sin x . cos x
cos 2x = cos²x – sin²x

2.Calculate functions of double argument if:

Solution:

3.Simplify:

Solution:

4.Simplify:

5.Calculate the trigonometric functions of the half angle if

6.Simplify:

7.Prove identity:

8.Prove identity:

9.Prove that it is valid:

10.Show that the identity holds:

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