Question

Express sin 65° + tan 57° in terms of trigonometric ratios of angles between 0° and 45°.

Answer 1

Given: Express sin 65° + tan 57°.

Step-wise calculation:

sin 65° = sin (90° – 25°)

= cos 25°

tan 57° = tan (90° – 33°) 

= cot 33°

= `1/ (tan 33^circ)`

= `(cos 33^circ)/(sin 33^circ)`

sin 65° + tan 57° = cos 25° + cot 33°

= `cos 25^circ + 1/(tan 33^circ)` 

= `cos 25^circ + (cos 33^circ)/(sin 33^circ)`, where the angles 25° and 33° lie between 0° and 45°.