Question

Obtain the values of the trigonometric functions of 75°, 15° and 105° and prove that

(i) tan 75° + cot 75° = 4

(ii) sin 105° + cos 105° = \(\frac{1}{\sqrt2}\)

(iii) Sec 15° + cosec15° = 2√6

Answer 1

sin(45° + 30°) = sin45°. cos30° + cos45° · sin 30° 

= \(\frac{1}{\sqrt2}\)\(\frac{\sqrt 3}{2}\) + \(\frac{1}{\sqrt2}\).\(\frac{1}{2}\)