If `tanx=3/4`, `piltxlt(3pi)/2,` find the value of `sin(x/2) , cos(x/2), tan(x/2)`.

Answer

`sin(x/2) = 3/sqrt(10)`

`cos(x/2) = -1/sqrt(10)`

`tan(x/2)= -3`

Explanation

Since `piltxlt(3pi)/2`, cos x is negative.

Also `pi/2 lt x/2 lt (3pi)/4`.

Therefore, `sin\ x/2` is positive and `cos\ x/2` is negative.

`sec^2x =1+tan^2x = 1+(3/4)^2 = 25/16`

`cos^2x = 16/25`

`cos x = -4/5`

`cosx=1-2sin^2 \ x/2`

`-4/5 = 1-2 sin^2\ x/2`

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