Question

Find the value of cot(7.5)°

Answer 1

By identity, cos(C) + cos(D) = 2cos{(C+D)/2}*cos{(C-D)/2}

and sin(C) - sin(D) = 2cos{(C+D)/2}*sin{(C-D)/2}

2) ==> [cos(C) + cos(D)]/[sin(C) - sin(D)] =
= 2cos{(C+D)/2}*cos{(C-D)/2}/ 2cos{(C+D)/2}*sin{(C-D)/2} = cot{(C-D)/2}

3) Thus, cot(7.5) = cot{(45-30)/2} = (cos45 + cos30)/(sin45-sin30)

= (1/√2 - √3/2)/(1/√2 - 1/2) = (2 - √6)/(2 - √2)

By rationalizing this is = √6 + √3 + √2 + 2 = 7.596 (nearly)