Trigonometry

 Trigonometric Identities

1. sinθ=1/cscθ$\text{sin}\theta =1\text{/}\text{csc}\theta$
2. cosθ=1/secθ$\text{cos}\theta =1\text{/}\text{sec}\theta$
3. tanθ=1/cotθ$\text{tan}\theta =1\text{/}\text{cot}\theta$
4. sin(900−θ)=cosθ$\text{sin}\left({90}^0-\theta \right)=\text{cos}\theta$
5. cos(900−θ)=sinθ$\text{cos}\left({90}^0-\theta \right)=\text{sin}\theta$
6. tan(900−θ)=cotθ$\text{tan}\left({90}^0-\theta \right)=\text{cot}\theta$
7. sin2θ+cos2θ=1${\text{sin}}^2\theta +{\text{cos}}^2\theta =1$
8. sec2θ−tan2θ=1${\text{sec}}^2\theta -{\text{tan}}^2\theta =1$
9. tanθ=sinθ/cosθ$\text{tan}\theta =\text{sin}\theta \text{/}\text{cos}\theta$
10. sin(α±β)=sinαcosβ±cosαsinβ$\text{sin}\left(\alpha \pm \beta \right)=\text{sin}\alpha \text{cos}\beta \pm \text{cos}\alpha \text{sin}\beta$
11. cos(α±β)=cosαcosβ∓sinαsinβ$\text{cos}\left(\alpha \pm \beta \right)=\text{cos}\alpha \text{cos}\beta \mp \text{sin}\alpha \text{sin}\beta$
12. tan(α±β)=tanα±tanβ1∓tanαtanβ$\text{tan}\left(\alpha \pm \beta \right)=\frac{\text{tan}\alpha \pm \text{tan}\beta }{1\mp \text{tan}\alpha \text{tan}\beta }$
13. sin2θ=2sinθcosθ$\text{sin}2\theta =2\text{sin}\theta \text{cos}\theta$
14. cos2θ=cos2θ−sin2θ=2cos2θ−1=1−2sin2θ$\text{cos}2\theta ={\text{cos}}^2\theta -{\text{sin}}^2\theta =2{\text{cos}}^2\theta -1=1-2{\text{sin}}^2\theta$
15. sinα+sinβ=2sin12(α+β)cos12(α−β)$\text{sin}\alpha +\text{sin}\beta =2\text{sin}\frac{1}{2}\left(\alpha +\beta \right)\text{cos}\frac{1}{2}\left(\alpha -\beta \right)$
16. cosα+cosβ=2cos12(α+β)cos12(α−β)