Вот тебе все формулы
</span></span></span><span><span><span>sin3x</span> = <span>3sinx - sin3x</span></span>4</span><span><span><span>cos3x</span> = <span>3cosx + cos3x</span></span>4</span><span><span><span>tg3x</span> = <span>3sinx - sin3x</span></span><span>3cosx + cos3x</span></span><span><span><span>ctg3x</span> = <span>3cosx + cos3x</span></span><span>3sinx - sin3x</span></span>Формулы тригонометрических функций в четвертой степени<span><span><span>sin4x</span> = <span>3 - 4cos2x + cos4x</span></span>8</span><span><span><span>cos4x</span> = <span>3 + 4cos2x + cos4x</span></span>8</span>
</span><span><span> + sinβ = 2sinα + β ∙ cosα - β</span><span>22</span></span><span><span>cosα + cosβ = 2cosα + β ∙ cosα - β</span><span>22</span></span>
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sinα ∙ sinβ = cos(α - β) - cos(α + β)</span>2</span><span><span>sinα ∙ cosβ = sin(α - β) + sin(α + β)</span>2</span><span><span>cosα ∙ cosβ = cos(α - β) + cos(α + β)</span>2</span><span><span>tgα ∙ tgβ = cos(α - β) - cos(α + β) = tgα + tgβ</span><span>cos(α - β) + cos(α + β)ctgα + ctgβ</span></span><span><span>ctgα ∙ ctgβ = cos(α - β) + cos(α + β) = ctgα + ctgβ</span><span>cos(α - β) - cos(α + β)tgα + tgβ</span></span><span><span>tgα ∙ ctgβ = sin(α - β) + sin(α + β)</span><span>sin(α + β) - sin(α - β)
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<span>sin2x + cos2x = 1</span>
<span><span><span>tgx</span> = <span>sinx</span></span><span>cosx</span></span><span><span><span>ctgx</span> = <span>cosx</span></span><span>sinx</span></span><span>tgx ctgx = 1</span>
<span><span><span>tg2x + 1</span> = 1</span><span>cos2x</span></span><span><span><span>ctg2x + 1</span> = 1</span><span>sin2x</span></span><span>sin2x = 2sinx cosx</span>
<span><span><span>sin2x</span> = <span>2tgx</span> = <span>2ctgx</span> = 2</span><span><span>1 + tg2x</span><span>1 + ctg2x</span><span>tgx + ctgx</span></span></span><span>cos2x = cos2x - sin2x = 2cos2x - 1 = 1 - 2sin2x</span>
<span><span><span>cos2x</span> = <span>1 - tg2x</span> = <span>ctg2x - 1</span> = <span>ctgx - tgx</span></span><span><span>1 + tg2x</span><span>ctg2x + 1</span><span>ctgx + tgx</span></span></span><span><span><span>tg2x</span> = <span>2tgx</span> = <span>2ctgx</span> = 2</span><span><span>1 - tg2x</span><span>ctg2x - 1</span><span>ctgx - tgx</span></span></span><span><span><span>ctg2x</span> = <span>ctg2x - 1</span> = <span>ctgx - tgx</span></span><span><span>2ctgx</span>2</span></span>Формулы тройного аргумента<span>sin3x = 3sinx - 4sin3x</span>
<span>cos3x = 4cos3x - 3cosx</span>
</span></span></span><span><span><span>sin3x</span> = <span>3sinx - sin3x</span></span>4</span><span><span><span>cos3x</span> = <span>3cosx + cos3x</span></span>4</span><span><span><span>tg3x</span> = <span>3sinx - sin3x</span></span><span>3cosx + cos3x</span></span><span><span><span>ctg3x</span> = <span>3cosx + cos3x</span></span><span>3sinx - sin3x</span></span>Формулы тригонометрических функций в четвертой степени<span><span><span>sin4x</span> = <span>3 - 4cos2x + cos4x</span></span>8</span><span><span><span>cos4x</span> = <span>3 + 4cos2x + cos4x</span></span>8</span>
sin(α + β) = sinα cosβ + cosα sinβ
cos(α + β) = cosα cosβ - sinα sinβ
sin(α - β) = sinα cosβ - cosα sinβ
cos(α - β) = cosα cosβ + sinα sinβ
</span><span><span> + sinβ = 2sinα + β ∙ cosα - β</span><span>22</span></span><span><span>cosα + cosβ = 2cosα + β ∙ cosα - β</span><span>22</span></span>
<span>(sinα + cosα)2 = 1 + sin2α</span>
<span><span>tgα + tgβ = sin(α + β)</span>cosα cosβ</span><span><span>ctgα + ctgβ = sin(α + β)</span>sinα sinβ</span>Формулы разности тригонометрических функций<span><span>sinα - sinβ = 2sinα - β ∙ cosα + β</span><span>22</span></span><span><span>cosα - cosβ = -2sinα + β ∙ sinα - β</span><span>22</span></span><span>(sinα - cosα)2 = 1 - sin2α</span>
<span><span>tgα - tgβ = sin(α - β)</span>cosα cosβ</span><span><span>ctgα - ctgβ = – sin(α - β)</span>sinα sinβ</span><span><span>
sinα ∙ sinβ = cos(α - β) - cos(α + β)</span>2</span><span><span>sinα ∙ cosβ = sin(α - β) + sin(α + β)</span>2</span><span><span>cosα ∙ cosβ = cos(α - β) + cos(α + β)</span>2</span><span><span>tgα ∙ tgβ = cos(α - β) - cos(α + β) = tgα + tgβ</span><span>cos(α - β) + cos(α + β)ctgα + ctgβ</span></span><span><span>ctgα ∙ ctgβ = cos(α - β) + cos(α + β) = ctgα + ctgβ</span><span>cos(α - β) - cos(α + β)tgα + tgβ</span></span><span><span>tgα ∙ ctgβ = sin(α - β) + sin(α + β)</span><span>sin(α + β) - sin(α - β)
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