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8.5: Appendix E- Mathematical Formulas
https://phys.libretexts.org/Courses/Joliet_Junior_College/JJC_-_PHYS_110/08%3A_Reference/8.05%3A_Appendix_E-_Mathematical_Formulas
sin( $\alpha \pm \beta$ ) = sin $\alpha$ cos $\beta$ ± cos $\alpha$ sin $\beta$ cos 2 $\theta$ = cos 2 $\theta$ − sin 2 $\theta$ = 2 cos 2 $\theta$ − 1 = 1 − 2 sin 2 $\theta$ \(\frac{...sin( $\alpha \pm \beta$ ) = sin $\alpha$ cos $\beta$ ± cos $\alpha$ sin $\beta$ cos 2 $\theta$ = cos 2 $\theta$ − sin 2 $\theta$ = 2 cos 2 $\theta$ − 1 = 1 − 2 sin 2 $\theta$ $\frac{d}{dx}$ sec x = tan x sec x $\int \frac{dx}{a^{2} − x^{2}}$ = $\frac{1}{2a}$ ln $\big| \frac{x + a}{x − a} \big|$ $\int \sqrt{a^{2} - x^{2}}$ dx = $\frac{x}{2} \sqrt{a^{2} - x^{2}} + \frac{a^{2}}{2} \sin^{−1} \frac{x}{a}$
13.1: Appendix F- Mathematical Formulas
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Introductory_Physics_II_(1112)/zz%3A_Back_Matter/06%3A_13.1%3A_Appendix_F-_Mathematical_Formulas
sin( $\alpha \pm \beta$ ) = sin $\alpha$ cos $\beta$ ± cos $\alpha$ sin $\beta$ cos 2 $\theta$ = cos 2 $\theta$ − sin 2 $\theta$ = 2 cos 2 $\theta$ − 1 = 1 − 2 sin 2 $\theta$ \(\frac{...sin( $\alpha \pm \beta$ ) = sin $\alpha$ cos $\beta$ ± cos $\alpha$ sin $\beta$ cos 2 $\theta$ = cos 2 $\theta$ − sin 2 $\theta$ = 2 cos 2 $\theta$ − 1 = 1 − 2 sin 2 $\theta$ $\frac{d}{dx}$ sec x = tan x sec x $\int \frac{dx}{a^{2} − x^{2}}$ = $\frac{1}{2a}$ ln $\big| \frac{x + a}{x − a} \big|$ $\int \sqrt{a^{2} - x^{2}}$ dx = $\frac{x}{2} \sqrt{a^{2} - x^{2}} + \frac{a^{2}}{2} \sin^{−1} \frac{x}{a}$

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