From the top of a cliff 100 metre high, the angles of depression of the top and bottom of a tower are 45⁰ and 60⁰ respectively. The height of the tower is

If 2ycos θ = xsin θ and 2xsec θ - ycosec θ = 3, then the value of x² + 4y² is

A person from the top of a hill observes a vehicle moving towards him at a uniform speed. It takes 10 minutes for the angle of depression to change from 45⁰ to 60⁰.

After this the time required by the vehicle to reach the bottom of the hill is

If (a²-b²) sin θ + 2abcos θ = a²+b², then tan θ = 

If sec θ + tan θ=m (>1), then the value of sin θ is (0⁰ < θ < 90⁰)

If xsin³ θ + ycos³ θ = sin θ cos θ and xsin θ – ycos θ = 0, then the value of x² + y² equals