Priklady.euMathematicsTrigonometryDouble and half argument

Double and half argument

1.Write formulas for double and half arguments:

Formulas:
sin 2x = 2x sin x . cos x
cos 2x = cos²x – sin²x
argument1

argument1

2.Calculate functions of double argument if:

argument2ak

Solution:

argument2r

3.Simplify:

argument2ak

Solution:

argument3r

4.Simplify:

argument2ak

Solution:

argument4r

5.Calculate the trigonometric functions of the half angle if

argument5ak

Solution:

argument5r

6.Simplify:

argument6

Solution:

argument6r

7.Prove identity:

argument7

Solution:

argument7r

Identita platí, ak x ≠ kπ

8.Prove identity:

argument8

Solution:

argument8r

Identity proved when x ≠ kπ

9.Prove that it is valid:

argument9

Solution:

argument9r

Identity proved when x ≠ kπ