Without using the trigonometric table, evaluate the following: 

$\mathrm{cosec} 35˚-\sec 55˚$

Without using the trigonometric table, evaluate the following: 

${\cos }^{2}26°+\cos 64°\sin 26°+ \frac{\tan {36}^{°}}{\cot 54°}$

Without using the trigonometric table, evaluate the following: 

$\frac{\sec 17°}{\cos ec {73}^{°}}+ \frac{\tan 68°}{\cot 22°}+ {\cos }^{2}44°+{\cos }^{2}46°$

Without using the trigonometric table, evaluate the following: 

$\frac{\cos 65°}{\sin 25°}+\frac{\cos 32°}{\sin 58°}-\sin 28°\sec 62°+ \cos ec 30°$

Without using the trigonometric table, evaluate the following:

$\frac{\sec 29°}{\mathrm{cosec} 61°}+2\cot 8° \cot 17°\cot 45°\cot 73° \cot 82°-3({\sin }^{2}38°+{\sin }^{2}52°)$

Express$\tan 81˚+\cos 72˚$  in terms of trigonometric ratios of angles between $0°$ to $45°$

Express $\cot 49˚+\mathrm{cosec} 87˚$  in terms of trigonometric ratios of angles between $0°$ to $45°$

Without using the trigonometric tables, prove that,

${\cos }^{2}25°+{\cos }^{2}65°=1$