Question

if cot x=-3/4 and x is not in the second quadrant then find 5 sin x+10cos x+9sec x+16cosec x-4cot x

Answer 1

cotx = -3/4

we know, cotx will be negative in 2nd or 4th quadrant. but questions said , " x is not in the 2nd quadrant .

so, x must be 4th quadrant .
e.g π< x < 3π/2

here sinx will he negative , but cosx will be positive .

hence,
sinx = -4/5
cosecx = -5/4
cosx = 3/5
secx = 5/3

now,
5sinx +10cosx +9secx +16cosecx -4cotx

= 5 × (-4/5) + 10 × 3/5 + 9×5/3 +16 × (-5/4) -4( -3/4)

= -4 + 6 +15 -20 +3

=-24 + 24

= 0