Express each of the following in terms trigonometric ratios of angles lying between 0° and 45°

Question

Express each of the following in terms trigonometric ratios of angles lying between 0\(^\circ\)and 45\(^\circ\)

(i) sin67\(^\circ\) + cos75\(^\circ\)

(ii) cot 65\(^\circ\)+ tan49\(^\circ\)

(iii) sec78\(^\circ\) + cosec56\(^\circ\)

(iv) cosec 54\(^\circ\) + sin 72\(^\circ\)

Answer 1

 (i) sin67\(^\circ\) + cos75\(^\circ\)

= cos(90\(^\circ\)- 67\(^\circ\)) + sin(90\(^\circ\)- 75\(^\circ\))

= cos23\(^\circ\) + sin 15\(^\circ\)

(ii) cot 65\(^\circ\)+ tan49\(^\circ\)

= cos(90\(^\circ\)- 65\(^\circ\)) + cot(90\(^\circ\)- 49\(^\circ\))

= cos25\(^\circ\) + cos41\(^\circ\)

(iii) sec78\(^\circ\) + cosec56\(^\circ\)

= sec(90\(^\circ\)- 12\(^\circ\)) + cosec(90\(^\circ\)- 34\(^\circ\))

= cosec12\(^\circ\) + sec34\(^\circ\)

(iv) cosec 54\(^\circ\) + sin 72\(^\circ\)

= sec(90\(^\circ\)- 54\(^\circ\)) + cos(90\(^\circ\)- 72\(^\circ\))

= sec36\(^\circ\) + sec18\(^\circ\)