Question

tanx=3/4,x lies in quadrant, find tanx/2&cosecx/2

Answer 1

Answer:

Step-by-step explanation:

Since x lies between 270° to 360° ie lies in 4th quadrant.

And in 4th quadrant sinx, tanx, cosec x are - ve. And cosx & secx are + ve.

tan x = -3/4 ( given)

Since, sec²x = 1+ tan² x

=> sec² x = 1 + 9/16

=> sec² x = 25/16

=> secx = 5/4 …………………..(1)

=> cos x = 4/5 ………………(2)

And, sin²x = 1- cos² x

=> sin x = √(1–16/25)

=> sinx = √(9/25)

=> sinx = -3/5 ……………..…….(3)

=> cosec x = - 5/3 …………………..(4)

Now, put up all these values in the given expression

(16–2sinx+cosx) ÷ ( 13+4secx + 6cosecx)

= (16 - 2* -3/5 +4/5) / (13+4*5/4 + 6*-5/3)

= (16+ 6/5 + 4/5) / (13 +5 -10)

= 18/8

= 9/4