If `sin(x+20^0)=2sinxcos40^0,where in (0,pi/2),` then which of the following hold(s) good? (a)`cos2x=1/2` (b) `cos e c4x=2` (c)`sec(x/2)=sqrt(6)-sqrt(2)` (d) `tan(x/2)=(2-sqrt(3))`

Explanation

`sinxcos20+cosxsin20=2sinxcos40`

`cosxsin20=sinx(2cos40-cos20)`

`tanx=(sin20)/(cos40+(cos40-cos20))`

`=(sin20)/(cos40+2sin30*sin(-10)`

`=(sin20)/(sin50-sin10)`

`=sin20/(2cos30sin20)`

`tanx=1/sqrt3`

`x=30`

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