Adding/Subtracting/Negating Angles of Trignometric Ratios

1. Following is the manner in which Trigonometric Ratios are affected when Adding/Subtracting Angles
   
   

   Angles	sin	cos	tan	cosec	sec	cot
   90°-θ	\(\cos\theta\)	\(\sin\theta\)	\(\cot\theta\)	\(\sec\theta\)	cosec \(\theta\)	\(\tan\theta\)
   90°+θ	\(\cos\theta\)	\(-\sin\theta\)	\(-\cot\theta\)	\(\sec\theta\)	\(-\)cosec \(\theta\)	\(-\tan\theta\)
   180°-θ	\(\sin\theta\)	\(-\cos\theta\)	\(-\tan\theta\)	cosec \(\theta\)	\(-\sec\theta\)	\(-\cot\theta\)
   180°+θ	\(-\sin\theta\)	\(-\cos\theta\)	\(\tan\theta\)	\(-\)cosec \(\theta\)	\(-\sec\theta\)	\(\cot\theta\)
   270°-θ	\(-\cos\theta\)	\(-\sin\theta\)	\(\cot\theta\)	\(-\sec\theta\)	\(-\)cosec \(\theta\)	\(\tan\theta\)
   270°+θ	\(-\cos\theta\)	\(\sin\theta\)	\(-\cot\theta\)	\(-\sec\theta\)	cosec \(\theta\)	\(-\tan\theta\)
   360°-θ	\(-\sin\theta\)	\(\cos\theta\)	\(-\tan\theta\)	\(-\)cosec \(\theta\)	\(\sec\theta\)	\(-\cot\theta\)
   360°+θ	\(\sin\theta\)	\(\cos\theta\)	\(\tan\theta\)	cosec \(\theta\)	\(\sec\theta\)	\(\cot\theta\)

   
   All the above Trignometric Ratios can be calculted using the Trignometric Identies of \(\sin(A \pm B)\) and \(\cos(A \pm B)\).
2. Following is the manner in which Trigonometric Ratios are affected when Angles are Negated
   
   

   \(\sin(-\theta)=-\sin(\theta)\)	\(\cos(-\theta)=\cos(\theta)\)	\(\tan(-\theta)=-\tan(\theta)\)
   cosec \((-\theta)=-\) cosec \((\theta)\)	\(\sec(-\theta)=\sec(\theta)\)	\(\cot(-\theta)=-\cot(\theta)\)