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We know that tanθ = sinθ/cosθ. Given 2sinθ = tanθ, we have 2sinθ = sinθ/cosθ. Multiplying both sides by cosθ, we get 2sinθ * cosθ = sinθ. Dividing both sides by sinθ, we get 2cosθ = 1. Thus, cosθ = 1/2. Now, sin²θ = 1 - cos²θ = 1 - (1/2)² = 1 - 1/4 = 3/4, so sinθ = √3/2.
If x4 + x2 y2 + y4 = 37 and x2 – xy + y2 = 5, then what is the value of xy ?
A solid cone and a solid hemisphere have the same radius and height. If the volume of the cone is 540 cm³, find the volume of the hemisphere.
Determine the volume of a cube if the total cost to paint its four walls is Rs. 1280, given that the painting rate is Rs. 5 per square meter.
The area of four walls of a room is 192 cm2. If the length and breadth of the room were equal and the height of the room is 6 cm, then what i...
Each side of square ‘A’ is 8 cm less than that of square ‘B’. The perimeter of a rectangle is 6 times the difference of the perimeters of the tw...
A circular wire of diameter 70 cm is folded in the shape of a rectangle whose sides are in the ratio 3:2. Find the area enclosed by the rectangle.
A cylindrical tank has a height of 12 meters and a radius of 7 meters. If 50% of the tank is filled with water, what is the volume of water in the tank ...
What is the difference between (in m2) the area of a circular field of radius 21 metres and area of a rectangular piece of land having its di...
The sum of length, breadth and height of cuboid is 20cm.If the length of the diagonal is 12 cm, then find the total surface area of the cuboid.
The length, breadth and height of a storeroom are 17m, 10m and 12m respectively. If each box occupies 40 m3 of space, then how many boxes can...
