Question

find the value of-
cos50/ 2sin40 + 4(cosec^2 59-tan^2 31)/ 3 tan^2 45 - 2/3 tan 12 tan 78 tan 90

Answer 1

$\frac{cos (50)}{2 sin (50)}= \frac{sin(90-50)}{2 sin(40)}= \frac{sin(40)}{2 sin(40)}=0.5$...(1)
$\frac{2}{3}tan(12)tan(78)tan(90)= \frac{2}{3}tan(12)cot(12)tan(90)= \frac{2}{3}tan(90)$....(2)
$4 \frac{cosec^2(59)-tan^2(31)}{3tan^2(45)-\frac{2}{3}tan(12)tan(78)tan(90)}=\\4 \frac{sec^2(31)-tan^2(31)}{3-\frac{2}{3}tan(90)}= \\4\frac{sec^2(31)-(sec^2(31)-1)}{3-\frac{2}{3}tan(90)}= \frac{12}{3-2tan(90)}=0$
...(3)
add (1) + (3)=0.5