Question
If 'θ' is an angle less than 120°, what is
the value of 'θ' if it satisfies the equation 3cos2θ = 2 + sin2θ.Solution
Given, 3cos2θ = 2 + sin2θ
Or, 3cos2θ - sin2 θ = 2
Or, 3cos2θ - (1 - cos2 θ) = 2
Or, 4cos2θ = 3
Or, cos2θ = (3/4)
Or, cosθ = √3/2 (Since, in options maximum value of 'θ' is 90o therefore, we will take the positive root only)
Or, cosθ = cos30o
So, θ = 30o
In a total 80-liter mixture of milk and water, there is 25% milk. How many liters of water should be added so that the quantity of milk in the mixture b...
A milkman mixed milk and water in an empty container in the ratio 14:9. The quantity of milk mixed was bought by the milkman at the rate of Rs. 25/litre...
In a mixture, the milk and water are in the ratio 9:2. When 44 liters of the mixture is replaced with 20 liters of water, the ratio becomes 9:4. Find t...
Quantity of water in a 350 litres mixture (Milk + Water) is 50 litres less than the quantity of milk in it. Find the quantity of water to be mixed so th...
- 360 litres of mixture 'P' has milk and water in the ratio 4:1, and 240 litres of mixture 'Q' has them in the ratio 5:3. What is the ratio of milk to water ...
(X + 140) liters of mixture A contains milk and water only such that quantity of water in it is (X – 100) liters less than quantity of milk in it. 75%...
A mixture contains liquid A and liquid B in the ratio of 5:3, respectively. If 12L of liquid B is added to this mixture, the respective ratio of liquid ...
In a 120-litre chemical mixture, the chemicals A and B are in the ratio 5:7. How much of chemical A must be added to make the ratio 7:7 (i.e., equal amo...
A vessel contains 200 litres of milk and water in the ratio of 5:3. If 10 litres of milk is added to the mixture, then find the ratio of milk to water i...
A mixture contains 30 ml water and rest ‘x’ ml milk. When 0.6x ml of water is added to the mixture, the quantity of water becomes 2/5th of the mixtu...
Relevant for Exams:
