If `tan( pi cos theta) = cot ( pi sin theta)` then `sin (theta + pi/4) ` equals

Explanation

Given,

`=>tan[picostheta]=cot[pisintheta]`

`=>tan[picostheta]=tan[pi/2−pisintheta]`

`=>picostheta=pi/2−pisintheta`

`=>(pi)[costheta+sintheta]=(pi)/2`

`=>costheta+sintheta=1/2`

dividing by `1/(sqrt2)`

`=>1/(sqrt(2))costheta+1/(sqrt(2))sintheta=1/(2sqrt(2))`

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