Question

2 sin 68 / cos 22 - 2 cot 15 / 5 tan 75 - 3 tan 45 tan 20 tan 40 tan 50 tan 70 /5
Evaluate the sum

Answer 1

before solving the following formula must be kept in mind
sin x = cos (90-x)
tan x = cot (90-x)
tan(x) × cot (x) =1
sin 68° = cos 22°
cot 15° = tan 75°
tan 45° = 1

tan 50°= cot 40° and tan 70° = cot 20°
the problem then reduce to 2

sin 68° / sin 68° - 2 , cot 15° /5 , cot 15° - 3 tan 20°
tan 40° , cot 40° , tan 40° /5 = 2-2/5-3/5=2-1=1