Chapter 7 - 7.2 - Verifying Trigonometric Identities - 7.2 Exercises - Page 521: 56

$tan^263°+cot^216°-sec^274°-csc^227°=-2$

Use $tan(\frac{\pi}{2}-u)=tan(90°-u)=cot~u$ and $cot(\frac{\pi}{2}-u)=cot(90°-u)=tan~u$ Also: $1+cot^2u=csc^2u$ $cot^2u-csc^2u=-1$ $1+tan^2u=sec^2u$ $tan^2u-sec^2u=-1$ $tan^263°+cot^216°-sec^274°-csc^227°=tan^2(90°-27°)+cot^2(90°-74°)-sec^274°-csc^227°=(cot^227°-csc^227°)+(tan^274°-sec^274°)=-1-1=-2$