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Question Number 4783 by Dnilka228 last updated on 10/Mar/16

cos α+β ≈(((cos α+cos β)/(cos^(−1) α+cos^(−1) β)))^(α+β)   sin a+b≈(((sin a+sin b)/(sin^(−1) a+sin^(−1) b)))^(a+b)   tan (a+(a/b))^k ≈(((tan (a+b)×k)/(tan^(−1) (a+b)×k)))

$$\mathrm{cos}\:\alpha+\beta\:\approx\left(\frac{\mathrm{cos}\:\alpha+\mathrm{cos}\:\beta}{\mathrm{cos}^{−\mathrm{1}} \alpha+\mathrm{cos}^{−\mathrm{1}} \beta}\right)^{\alpha+\beta} \\ $$$$\mathrm{sin}\:{a}+{b}\approx\left(\frac{\mathrm{sin}\:{a}+\mathrm{sin}\:{b}}{\mathrm{sin}^{−\mathrm{1}} {a}+\mathrm{sin}^{−\mathrm{1}} {b}}\right)^{{a}+{b}} \\ $$$$\mathrm{tan}\:\left({a}+\frac{{a}}{{b}}\right)^{{k}} \approx\left(\frac{\mathrm{tan}\:\left({a}+{b}\right)×{k}}{\mathrm{tan}^{−\mathrm{1}} \left({a}+{b}\right)×{k}}\right) \\ $$

Commented by Dnilka228 last updated on 10/Mar/16

sin (a+(a/b))^Γ ≈(((sin (a+b)×Γ)/(sin^(−1) (a−b)÷Γ)))  cos (Γ=e+(π/2))^(α+β) ≈(((cos e+cos (π/2))/(cos^(−1) e−cos^(−1) (π/2))))

$$\mathrm{sin}\:\left({a}+\frac{{a}}{{b}}\right)^{\Gamma} \approx\left(\frac{\mathrm{sin}\:\left({a}+{b}\right)×\Gamma}{\mathrm{sin}^{−\mathrm{1}} \left({a}−{b}\right)\boldsymbol{\div}\Gamma}\right) \\ $$$$\mathrm{cos}\:\left(\Gamma={e}+\frac{\pi}{\mathrm{2}}\right)^{\alpha+\beta} \approx\left(\frac{\mathrm{cos}\:{e}+\mathrm{cos}\:\frac{\pi}{\mathrm{2}}}{\mathrm{cos}^{−\mathrm{1}} {e}−\mathrm{cos}^{−\mathrm{1}} \frac{\pi}{\mathrm{2}}}\right) \\ $$

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