Question
If sin (3A − 2B) = (√3/2) and cos (A + B) = (1/2),
where 0° < A, B < 90°, then find the value of ‘A’.Solution
sin (3A − 2B) = (√3/2)
Or, sin (3A − 2B) = sin 60°
Or, 3A − 2B = 60° ----------- (I)
And, cos (A + B) = (1/2)
Or, cos (A + B) = cos 60°
Or, A + B = 60° -------------- (II)
On solving equation I + 2 × equation II, we get;
3A − 2B + 2 × (A + B) = 60 + 2 × 60
Or, 3A − 2B + 2A + 2B = 180°
Or, 5A = 180°
So, ‘A’ = 36°
Two trains P and Q of lengths 250 m and 400 m, respectively, are running in the same direction on parallel tracks at 90 km/h and 120 km/h, respectively....
A goods train leaves a station at a certain time and at a fixed speed. After 10 hours, an express train leaves the same station and moves in the same di...
A train 270 metre long takes 36 sec to cross a man running at a speed of 4 km/hr in the direction opposite to that of train. What is the speed of the tr...
- Two stations P and Q are 486 km apart. A train leaves P at 6:45 a.m. at 54 km/h. Another train leaves Q at 8:15 a.m. towards P at 81 km/h. When will they m...
Train ‘A’ running with a speed of 108 km/hr crosses a vertical pole in 10 seconds. Find the approx. time taken by the train ‘A’ ...
Train 'K' leaves at 6:00 PM on Saturday from Ahmedabad station and reaches Surat station at 8:00 AM the next day, while train 'L' leaves at 7:00 PM on S...
Two trains of same length are running in parallel tracks in the same direction with speed 40 km/hr and 100 km/hr respectively. The latter completely cro...
A train travels at an average speed of 100 km per hour without stoppage and with stoppages it covers the same distance at an average speed of 80 km/hr. ...
A train has to cover a distance of 112 km in 14 hours. If it covers half journey in 3/5th time, then the speed of covering the remaining dist...
A train running with a speed of 117 km/hr can cross a pole in 19 seconds and a platform in 23 seconds. Find the length of the platform.
Relevant for Exams:
