The P.E gained by projectile when it reaches at maximum height is expressed by equation;

Explanation

Option C is correct. At maximum height, the projectile's vertical velocity is zero, and its potential energy (PE) is maximized. The potential energy gained is equal to the initial kinetic energy (K.E.) associated with the vertical component of the initial velocity, which is given by K.E. sin²θ. This is because the vertical component of the initial velocity is vo sin θ, and the energy associated with this component is transferred into potential energy at the peak. Option A is incorrect because cosine pertains to horizontal motion. Option B is incorrect because tangent refers to a ratio of vertical to horizontal components, not directly to potential energy. Option D is incorrect as cotangent is the reciprocal of tangent and does not relate to maximum height or potential energy.