Question
If tan A = 1 and tan B = β 3, what is the value of cos
A . cos B - sin A . sin B?Solution
Given, tan A = 1 β A = 45Β° Also given, tan B = β 3 β B = 60Β° β΄ cos A . cos B - sin A . sin B = cos 45Β° . cos 60Β° - sin 45Β° . sin 60Β° = 1/ β 2 * 1/2 - 1/ β 2 . β 3/2 = (1 - β 3)/2 β 2
Individuals A and B have their incomes in the ratio of 5 to 3, while the ratio of their expenditures stands at 3 to 4, respectively. A saves Rs. 43,000 ...
In a shop, there are a total of 15,000 chip packets. Out of these, 28% are Green Lays packets, and out of the remaining, 75% are Red Lays packets, and t...
The population of a city is decreased by 20% in the first year and then increased by 30% in the second year. Find the population of the cityΒ at the end...
Anita spends 75% of her monthly salary and receives a commission of 5% on her salary every month. If her annual saving is Rs. 129600, find the commissio...
In a mixed school 25% of the scholars are infants under 7 and the number of girls above 7 is 4/5 of the number of boys above 7, is 120. Find the number ...
In a college the ratio of boys and girls are in the ratio 7:9. 65% girls and 40% boys were absent. Find the girls present if the total number of student...
Divakar spends 30% of his salary on house rent, 20% of the remaining amount on shopping, 25% of the remaining on education fees, and the rest is divided...
The income of a person is Rs.15000 and his expenditure is Rs.12000. In the next year his income and expenditure is increased by 8% and 13% respectively....
- In a qualifying test, the passing marks are 60%. Marks obtained by βGβ are 5% less than passing marks, and βHβ scores 28% marks less than G. What p...
A pear has a cylindrical-shaped seed exactly in the center. If the diameter and height of the seed are both equal to one-fifth of the diameter of the fr...