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If tanx=3/4, piltxlt(3pi)/2, find the v...

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

Text Solution

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The correct Answer is:
`sin(x/2) = 3/sqrt(10)`
`cos(x/2) = -1/sqrt(10)`
`tan(x/2)= -3`
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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