S L Loney Solutions for Chapter: Trigonometrical Ratios of Angles of any Size and Sign, Exercise 1: EXAMPLES X

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

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

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

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

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

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

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