Find the equation of the tangent to the curve `x=theta+sintheta,y=1+costheta`, at `theta=pi/4`

Explanation

To find equation of the tangent, we need slope and one point on the tangent. point on the tangent at `theta=frac{pi}{4}`

`x=frac{pi}{4}+sin (frac{pi}{4})=frac{pi}{4}+frac{1}{sqrt{2}}`


and


`y=1+cos(frac{pi}{4})=1+frac{1}{sqrt{2}}`

Therefore point `P(frac{pi}{4}+frac{1}{sqrt{2}}`, `1+frac{1}{sqrt{2}})` lies on the line.

To find the slope, we find`frac{d y}{d x}`

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