JEE Main & Advanced Mathematics Trigonometrical Ratios and Identities Trigonometrical Ratios of Allied Angles

Trigonometrical Ratios of Allied Angles

Category : JEE Main & Advanced

Two angles are said to be allied when their sum or difference is either zero or a multiple of \[{{90}^{o}}\].    

Allied angles \[\to \] \[\sin \theta \] \[cos\theta \] \[tan\theta \]
Trigo. Ratio
\[\downarrow \,\,(-\theta )\] \[-\sin \theta \] \[cos\theta \] \[-tan\theta \]
\[(90-\theta )\] or \[\left( \frac{\pi }{2}-\theta  \right)\] \[cos\theta \] \[\sin \theta \] \[\cot \,\theta \]
\[(90-\theta )\] or \[\left( \frac{\pi }{2}-\theta  \right)\] \[\cos \theta \] \[-\,\sin \theta \] \[-\cot \,\theta \]
\[(180-\theta )\] or\[(\pi -\theta )\] \[\sin \theta \] \[-\,\cos \theta \] \[-tan\theta \]
\[(180+\theta )\] or \[(\pi -\theta )\] \[-\,\sin \theta \] \[-\,\cos \theta \] \[tan\theta \]
\[(270-\theta )\]or \[\left( \frac{3\pi }{2}-\theta  \right)\] \[-\,\cos \theta \] \[-\,\sin \theta \] \[\cot \,\theta \]
\[(270+\theta )\] or \[\left( \frac{3\pi }{2}-\theta  \right)\] \[-\,\cos \theta \] \[\sin \theta \] \[-\cot \,\theta \]
\[(360-\theta )\] or \[(2\pi -\theta )\] \[-\,\sin \theta \] \[cos\theta \] \[-tan\theta \]

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