(i) Shown below is a horizontal water tank composed of a cylinder and two hemispheres. The tank is filled up to a height of 7 m. Find the surface area of the tank in contact with water. Use π = 22/7
(ii) In a recurring deposit account for 2 years, the total amount deposited by a person is ₹ 9600. If the interest earned by him is one-twelfth of his total deposit, then find:
(a) the interest he earns.
(b) his monthly deposit.
(c) the rate of interest.
(iii) Find:
(a) (sin 𝜃 + 𝑐𝑜𝑠𝑒𝑐 𝜃) 2
(b) (𝑐𝑜𝑠 𝜃 + 𝑠𝑒𝑐 𝜃) 2
Using the above results prove the following trigonometry identity.
(sin 𝜃 + 𝑐𝑜𝑠𝑒𝑐 𝜃) 2 + (cos 𝜃 + sec 𝜃) 2 = 7 + 𝑡𝑎𝑛2𝜃 + 𝑐𝑜𝑡2𝜃
Solution
,
,