# Half Angle Formula

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

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### Re: Half Angle Formula

Please, look at the formulas here:
Power-Reducing Formulas

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### Re: Half Angle Formula

Formulas of degrees lowering : $$sin^{2}$$$$\alpha$$=$$\frac{1-cos(2\alpha)}{2}$$ ; $$cos^{2}$$$$\alpha$$=$$\frac{1+cos(2\alpha)}{2}$$

$$sin^{4}$$(2x)=$$(sin^{2}(2x) )^{2}$$=$$[\frac{1-cos(2.2x)}{2}]^{2}$$=[$$\frac{1-cos(4x)}{2}]^{2}$$=

=$$\frac{1-2cos(4x)+cos^{2}(4x)}{4}$$=$$\frac{1}{4}$$-$$\frac{2cos(4x)}{4}$$+$$\frac{cos^{2}(4x)}{4}$$=

=$$\frac{1}{4}$$-$$\frac{1}{2}$$cos(4x)+$$\frac{\frac{1+cos(2.4x)}{2}}{4}$$=$$\frac{1}{4}$$-$$\frac{1}{2}$$cos(4x)+$$\frac{1+cos(8x)}{8}$$=$$\frac{1}{4}$$-$$\frac{1}{2}$$cos(4x)+$$\frac{1}{8}$$+$$\frac{cos(8x)}{8}$$=

=$$\frac{3}{8}$$-$$\frac{1}{2}$$cos(4x)+$$\frac{1}{8}$$cos(8x)
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