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Trigonometric Addition Formulae

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☼ Trigonometric Addition Formulae : –

sin ( $\alpha+\beta$ ) = sinα cosβ + cosα sinβ

sin ( $\alpha-\beta$ ) = sinα cosβ – cosα sinβ

tan ( $\alpha+\beta$ ) = $\frac{tan{\alpha}+tan{\beta}}{1-tan{\alpha}\ tan{\beta}}$

tan ( $\alpha-\beta$ ) = $\frac{tan{\alpha}-tan{\beta}}{1+tan{\alpha}\ tan{\beta}}$

cos ( $\alpha+\beta$ ) = cosα cosβ – sin α sinβ

cos ( $\alpha-\beta$ ) = cosα cosβ + sin α sinβ

cot ( $\alpha+\beta$ ) = $\frac{cot{\alpha}\ cot{\beta}-1}{cot{\beta}+cot{\alpha}}$

cot ( $\alpha-\beta$ ) = $\frac{cot{\alpha}\ cot{\beta}+1}{cot{\beta}-cot{\alpha}}$