P & Q are the points with eccentric angles `theta`&`theta+pi/6`on the elipse `x^2/16 + y^2/4 =1`,then area of triangle OPQ is

Explanation

Coordinates of point `P` will be `(acostheta,bsintheta)`.

Coordinates of point `Q` will be `(acos(theta+pi/6),bsin(theta+pi/6))`.

Here, `O` is origin.

`:.` Area of `Delta OPQ`,

`A = 1/2|[acostheta,bsintheta,1],[acos(theta+pi/6),bsin(theta+pi/6),1],[0,0,1]|`

`=>A = 1/2[acosthetabsin(theta+pi/6) - acos(theta+pi/6)bsintheta]`

`=>A = 1/2ab[sin((theta+pi/6)-theta)]`

`=>A = 1/2ab sin (pi/6)`

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