Trigonometry: calculate sin^4 \alpha - cos^4 \alpha = 0

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

Trigonometry: calculate sin^4 \alpha - cos^4 \alpha = 0

Postby kate » Fri Jul 04, 2008 11:59 am

Calculate:

[tex]sin^4 \alpha - cos^4 \alpha = 0[/tex]
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Re: Trigonometry: calculate sin^4 \alpha - cos^4 \alpha = 0

Postby Guest » Wed Sep 28, 2011 8:34 am

[tex]sin^4\alpha - cos^4\alpha = 0[/tex]

[tex](sin^2\alpha - cos^2\alpha)(sin^2\alpha + cos^2\alpha) = 0[/tex]

From the basic trigonometric identity:
[tex]sin^2\alpha + cos^2\alpha = 1[/tex]

[tex]sin\alpha = \pm cos\alpha[/tex]
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