Question

What is the equation of the line tangent to `f(x)=sin x + sin^2 x` at `x=0`?

Answer 1

The equation of tangent is `y=x`

Explanation:

`f(x)=sinx+sin^2x ; x=0`

`:. f(0)=sin0+sin^2(0)= 0`

Point in the curve is `(0,0)`

`f(x)=sinx+sin^2x`

`f'(x)= cosx+ 2sinxcosx`

`f'(0)= cos 0+ 2sin0cos0`

`f'(0)= 1+ 0=1`

Slope at the point `(0,0)` is `1`

The equation of tangent at the point is `(y-0)=1(x-0)` or

`y=x` .Therefore the equation of tangent is `y=x` [Ans]