Explanation
x=a(θ+sinθ)
y=a(1+cosθ)
If tangent to curve at θ=π/3, makes angle α with x-axis,
⇒ slope of tangent = tanα
⇒ tanα=dy/dθdx/dθ|θ=π/3
=−asinθa(1+cosθ)
−sinθ1+cosθ|θ=π/3
=−√3/21+1/2
tanα =−1√3
Ans. α = 5π/6
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