Find the value of: (i) sin 75° (ii) tan 15°

i) sin 75° = sin (90° - 15°) = cos 15°
Using the identity sin(90° - A) = cos A
cos A/2 = √(1 + cos A)/2
Put A = 30° in the above identity
Therefore, cos 15° = √(1 + cos 30°)/2 = √(√3 + 2)/2
ii) tan 15° = √(sec²15° - 1) = √(1/cos²15° - 1) = √(2 - √3)/(2 + √3) from (i)