Supplementary Angles

Prove that: $\cot A+\tan \left({180}^{\circ }+A\right)+\tan \left({90}^{\circ }+A\right)+\tan \left({360}^{\circ }-A\right)=0$.

Prove that: $\sec \left({270}^{\circ }-A\right)\sec \left({90}^{\circ }-A\right)-\tan \left({270}^{\circ }-A\right)\tan \left({90}^{\circ }+A\right)+1=0$.

Prove that $\cos A+\sin \left({270}^{\circ }+A\right)-\sin \left({270}^{\circ }-A\right)+\cos \left({180}^{\circ }+A\right)=0$.

Prove that: $\cos \left(270°-A\right)=-\sin A$ and $\cot \left(270°-A\right)=\tan A$.

Prove that: $\sin \left({270}^{\circ }+A\right)=-\cos A$ and $\tan \left({270}^{\circ }+A\right)=-\cot A$.

Find the sines and cosines of all angles in the first four quadrants whose tangents are equal to $\cos 135°$.

What sign $\sin A-\cos A$ has for the value of $A=-457°$?

What sign has $\sin A-\cos A$ for the following value of $A=-634°$?

What sign has $\sin A-\cos A$ for the following value of $A=825°$?

What sign $\sin A-\cos A$ has for the value of $A={215}^{\circ }$?

What sign has $\sin A+\cos A$ for the following value of $A=-1125°$?

What sign has $\sin A+\cos A$ for the following value of $A=-{356}^{\circ }$?

What sign has $\sin A+\cos A$ for value of $A={278}^{\circ }$?

What sign has $\sin A+\cos A$ for the following value of $A={140}^{\circ }$?

Express $\mathrm{cosec}\left(-756°\right)$ in terms of the ratios of a positive angle, which is less than $45°$.

Express $\sec 1327°$ in terms of the ratios of a positive angle, which is less than $45°$.

Express $\cot \left(-1054°\right)$ in terms of the ratios of a positive angle, which is less than $45°$.

Express in terms of the ratios of a positive angle, which is less than ${45}^{\circ }$, the quantity $\cos {1410}^{\circ }$.

Express $\tan 1145°$ in terms of the ratios of a positive angle, which is less than $45°$.

Express in terms of the ratios of a positive angle, which is less than ${45}^{\circ }$, the quantity $\cos \left(-{928}^{\circ }\right)$.