Question

pls guys do fast pls



its urgent

if tan x=3/4, pie<x<3 pie/2

find the. value of

sin x/2,cosx/2 and tan x/2

Answer 1

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$\huge{ \mathfrak{here \: is \: answer}}$


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Answer 2

Heya,

We know that,
Sec²x = 1+tan²x
Sec²x = 1+(3/4)²
Sec²x = 1+(9/16)
Sec²x = 25/16
Secx = +- √25/16
Secx = +- 5/4

Since, π < x < 3π/2, It belongs to III quadrant in which Secx is negative

So,
Secx = -5/4
Cosx = -4/5

We have to know values of x/2
π < x < 3π/2 
then, 
π/2 < x/2 < 3π/2x2
π/2 < x/2 < 3π/4

So, x/2 belongs to II quadrant

So, Sinx/2 > 0, Cosx/2 < 0

1) 2Sin²x/2 = (1-cosx) = (1+4/5) = 9/5
      Sin²x/2 = 9/10
      Sinx/2 = +- √9/10
      Sinx/2 = +- 3/√10

    Since x/2 belongs II quad, Sinx/2 > 0
    Sinx/2 = 3/√10

2) 2Cos²x/2 = 1+Cosx = 1-4/5 = 1/5
      Cos²x/2 = 1/10
      Cosx/2 = +- 1/√10

   Since x/2 belongs to II quad, Cosx/2 is negative
       Cos x/2 = -1/√10

3) tanx/2 = Sinx/2 / Cos x/2
               = 3/√10 / -1/√10
               = -3
    
   Since x/2 belongs to II quad, tan x/2 is negative
   tanx/2 = -(-3)
   tanx/2 = 3

HOPE IT HELPS:-))