Trigonometrical Equations With Their General Solution
Category : JEE Main & Advanced
| Trigonometrical equation | General solution |
| \[\sin \theta =0\] | \[\theta =n\pi \] |
| \[\cos \theta =0\] | \[\theta =n\pi +\pi /2\] |
| \[\tan \theta =0\] | \[\theta =n\pi \] |
| \[\sin \theta =1\] | \[\theta =2n\pi +\pi /2\] |
| \[\cos \theta =1\] | \[\theta =2n\pi \] |
| \[\sin \theta =\sin \alpha \] | \[\theta =n\pi +{{(-1)}^{n}}\alpha \] |
| \[\cos \theta =\cos \alpha \] | \[\theta =2n\pi \pm \alpha \] |
| \[\tan \theta =\tan \alpha \] | \[\theta =n\pi \pm \alpha \] |
| \[{{\sin }^{2}}\theta ={{\sin }^{2}}\alpha \] | \[\theta =n\pi \pm \alpha \] |
| \[{{\tan }^{2}}\theta ={{\tan }^{2}}\alpha \] | \[\theta =n\pi \pm \alpha \] |
| \[{{\cos }^{2}}\theta ={{\cos }^{2}}\alpha \] | \[\theta =n\pi \pm \alpha \] |
| \[\left. \begin{align} & \sin \theta =\sin \alpha \\ & \cos \theta =\cos \alpha \text{ } \\ \end{align} \right|\text{ * }\] | \[\theta =2n\pi +\alpha \] |
| \[\left. \begin{align} & \sin \theta =\sin \alpha \\ & \tan \theta =\tan \alpha \text{ } \\ \end{align} \right|\text{ * }\] | \[\theta =2n\pi +\alpha \] |
| \[\left. \begin{align} & \tan \theta =\tan \alpha \\ & \cos \theta =\cos \alpha \text{ } \\ \end{align} \right|\text{ * }\] | \[\theta =2n\pi +\alpha \] |
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