Question
If SecA + TanA = 2√2 + 9, then find the value of
Sin A + Cos A.Solution
Sec²A – Tan²A = 1 (SecA – TanA) (SecA + TanA) = 1 (SecA – TanA) (2√2 + 9) = 1 (SecA - TanA) = 1/(2√2 + 9) SecA – TanA = 9 - 2√2 ………………(i) SecA + TanA = 9 + 2√2 ……………… (ii) By solving the two equations we get, 2SecA = 18 SecA = 9 CosA = 1/9 Sin²A + Cos²A = 1 Sin²A + 1/81 = 1 Sin²A = 1 - 1/81 Sin²A = 80/81 SinA= (4√5)/9 SinA + CosA = (4√5)/9+ 1/9 SinA + CosA = (1+4√5)/9
A merchant mixes two varieties of rice of 6 kg and 4 kg, which cost him Rs. 7 and Rs. 5 per kg, respectively. What is the cost price (in Rs.) of the mix...
A mixture contains ‘x’% milk. 30% of this mixture is taken out and is replaced with same quantity of water. This procedure is repeated two more time...
A mixture of 512 ml contains milk and whey protein in the ratio of 9:7, respectively. When 'p' ml of whey protein and (p + 36) ml of milk are added to t...
A container has only two types (P and Q) of oil in the ratio 3:2 respectively. When 90 litre of oil Q is added to the container the quantity of oil P be...
161 litres mixture of milk and water is mixed in an empty container in the ratio 5:2, respectively. If 14 litres of mixture is replaced with 14 litres o...
Mixture 'A' consists of 'm' liters of milk, while mixture 'B' includes '11 + m' liters of milk. Determine the ratio in which mixture 'B' to mixture 'A' ...
Two alloys are combined to create a new alloy. The first alloy contains 20% copper, and the second alloy contains 40% copper. If the resulting alloy has...
"A 480-liter mixture of alcohol and water has alcohol and water in the ratio of 5: p. When 20 liters of water are added, the new ...
Mixture 'A' has only petrol and diesel in the ratio 5:4 respectively and mixture 'B has only petrol and diesel in the ratio 3:2 respectively. Mixtures '...
The diluted wine contains only 8 liters of wine, and the rest is water. A new mixture whose concentration is 30%, is to be formed by replacing wine. How...
Relevant for Exams:
