Chhatrapati Shivaji Maharaj, the founder of the Maratha Empire, had a multifaceted relationship with the Portuguese, characterized by both diplomacy and military confrontation. The Portuguese were one of the colonial powers present along India’s western coastline, which brought them into conflict with Shivaji.
In conclusion, Shivaji’s relationship with the Portuguese was a mix of diplomatic negotiation, rivalry, and military confrontation, as he worked to secure Maratha control over vital coastal regions.
The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.
Solve the following L.P.P. by graphical method:
Maximize:
\[ z = 10x + 25y. \] Subject to: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]