# 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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