Find the value of `sin(1/2cot^(-1)(-3/4))`

1.	Find the value of `sin(1/2cot^(-1)(-3/4))`
Answer» `cot^(-1)(-3/4)=theta` `costheta=-3/5` `sinn(1/2theta)` `sin(theta/2)` `costheta=-3/5` `1-2sin^2(theta/2)=-3/5` `1+3/5=2sin^2(theta/2)` `2si^2(theta/2)=8/5` `sin^2(theta/2)=4/5` `sintheta=2/sqrt5,-2/sqrt5``-2/sqrt5` is not possible.

Discussion

`tan^(-1)[(cosx)/(1+sinx)]`is equal to`pi/4-x/2,forx in (-pi/2,(3pi)/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-(3pi)/2,pi/2)`
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