Eliminate & from the following: 2x = 3 - 4tan θ, 3y = 5 + 3sec θ..


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A particle is projected over a triangle from one end of a horizontal base and grazing the vertex falls on the other end of the base. If and β be the base angles and 8 the angle of projection, prove tan tanα + tanβ:


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The x and y coordinates of the particles at any time are x = 5t - 2t² and y = 10t respectively, where x and y are in metres and t in seconds. The acceleration of the particle at t = 2s is..


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A fighter plane flying horizontally at an altitude of 1.5 km with a speed 720 kmh passes directly overhead an antiaircraft gun. At what angle from the vertical should the gun be fired for the shell muzzle speed 600 ms to hit the plane? At what maximum altitude…

If sinA/3 = sinB/4 = 1/5 and A and B are the angles in the second quadrant, then prove that 4 cosA + 3 cosB = -5


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If cos x + sin x = √2 sin x,
show that cos x - sin x = √2 sin x

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if cosec θ - sin θ = x^3, sec θ - cos θ = y^3 show that x^2 y^2 ( x^2 y^2 ) = 1..


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1 - sec θ + tan θ / 1 + sec θ + tan θ = sec θ + tan θ - 1 / sec θ + tan θ + 1


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A body is projected at t = 0 with a velocity 10ms at an angle of 60° with the horizontal. The radius of curvature of its trajectory at t = Is is R. Neglecting air resistance and taking acceleration due to gravity g = 10ms, the value of R is..


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A particle is moving along the x-axis with its coordinate with time 't' given by x(t)=10+8t-3t. Another particle is moving along the y-axis with its coordinate as a function of time given by y(t)=5-8t. At t-is, the speed of the second particle as measured…