Prove that :

tan A + cot A = sec A. cosec A.

A cylindrical vessel of diameter 14 cm and height 42 cm is fixed symmetrically inside a similar vessel of radius 8 cm and height 42 cm. The total space between the two vessels is filled with glass-wool for heat insulation. Find the volume of the glass-wool required.

Use graph paper for this question. Take 1 cm = 1 unit on both x and y axis.

(i) Plot the following points on your graph sheets :

A(-4, 0), B(-3, 2), C(0, 4), D(4, 1) and E(7, 3).

(ii) Reflect the points B, C, D and E on the x-axis and name them as B', C', D' and E' respectively.

(iii) Join the points A, B, C, D, E, E', D', C', B' and A in order.

(iv) Name the closed figure formed.

For the inter-state supply of the following goods/services, find the amount of bill :