What is the value of tanπ4+A×tan3π4+A ?

What is the value of [(cos32θ + 3 cos 2θ)÷(cos6θ – sin6θ)]?

What is the value of [(sin 7x – sin 5x)÷(cos 7x + cos 5x)] – [(cos 6x – cos 4x)÷(sin 6x + sin 4x)]?

A regular square pyramid has side of its base 20 cm and height 45 cm is melted and recast into regular triangular pyramids of equilateral base of side 10 cm and height 10√3 cm. What are the total numbers of regular triangular pyramid?

A solid cube is cut into 27 identical cubes. What is the percentage increase in the total surface area?

Three toys are in a shape of cylinder, hemisphere and cone. The three toys have same base. Height of each toy is 2√2 cm. What is the ratio of the total surface areas of cylinder, hemisphere and cone respectively?

Two spheres of equal radius are taken out by cutting from a solid cube of side (12 + 4√3) cm. What is the maximum volume (in cm3) of each sphere?

A right circular cylinder has height 28 cm and radius of base 14 cm. Two hemispheres of radius 7 cm each are cut from each of the two bases of the cylinder. What is the total surface area (in cm2) of the remaining part?