e 44자리#

2.7182818284 5904523536 0287471352 6624977572 4709369995

시카노코노코 COS TAN TAN#

1. $\sin(x + y) = \sin(x) \cos(y) + \cos(x) \sin(y)$

2. $\cos(x + y) = \cos(x) \cos(y) - \sin(x) \sin(y)$

3. $\sin(2x) = 2 \sin(x) \cos(x)$

4. $\cos(2x) = \cos^2(x) - \sin^2(x) = 2 \cos^2(x) - 1 = 1 - 2 \sin^2(x)$

5. $\tan(2x) = \dfrac{2 \tan(x)}{1 - \tan^2(x)}$

6. $\sin(3x) = 3 \sin(x) - 4 \sin^3(x)$

7. $\cos(3x) = 4 \cos^3(x) - 3 \cos(x)$

8. $\sin(x + y) + \sin(x - y) = 2 \sin(x) \cos(y)$

9. $\sin(x + y) - \sin(x - y) = 2 \cos(x) \sin(y)$

10. $\cos(x + y) + \cos(x - y) = 2 \cos(x) \cos(y)$

11. $\cos(x + y) - \cos(x - y) = -2 \sin(x) \sin(y)$

12. $\sin(x) + \sin(y) = 2 \sin\left(\dfrac{x + y}{2}\right) \cos\left(\dfrac{x - y}{2}\right)$

13. $\sin(x) - \sin(y) = 2 \cos\left(\dfrac{x + y}{2}\right) \sin\left(\dfrac{x - y}{2}\right)$

14. $\cos(x) + \cos(y) = 2 \cos\left(\dfrac{x + y}{2}\right) \cos\left(\dfrac{x - y}{2}\right)$

15. $\cos(x) - \cos(y) = -2 \sin\left(\dfrac{x + y}{2}\right) \sin\left(\dfrac{x - y}{2}\right)$

16. $\cos^2(x) = \dfrac{1 + \cos(2x)}{2}$

17. $\sin^2(x) = \dfrac{1 - \cos(2x)}{2}$

18. $\tan^2(x) = \dfrac{1 - \cos(2x)}{1 + \cos(2x)}$

19. $\sin \alpha=\dfrac{a}{\sqrt{a^2+b^2}},\ \cos a =\dfrac{b}{\sqrt{a^2+b^2}}, \\ \sin \beta=\dfrac{b}{\sqrt{a^2+b^2}},\ \cos \beta=\dfrac{a}{\sqrt{a^2+b^2}}\ 일 때, \\ a\sin x+b\cos x=\sqrt{a^2+b^2}\Bigg(\dfrac{a}{\sqrt{a^2+b^2}}\sin x+\dfrac{b}{\sqrt{a^2+b^2}}\cos x\Bigg) \\ = \sqrt{a^2+b^2}(\sin\alpha \sin x+\cos\alpha\cos x)=\sqrt{a^2+b^2}\sin(x-\alpha) \\ a\sin x+b\cos x=\sqrt{a^2+b^2}\Bigg(\dfrac{a}{\sqrt{a^2+b^2}}\sin x+\dfrac{b}{\sqrt{a^2+b^2}}\cos x\Bigg) \\ = \sqrt{a^2+b^2}(\cos \beta \sin x+\sin \beta\cos x)=\sqrt{a^2+b^2}\sin(x+\beta)$