Question
The value of (1 + sin⁴ A – cos⁴ A) cosec² A
is:Solution
To simplify (1 + sin⁴ A – cos⁴ A) cosec² A Use cos4 A = (1- sin² A) ² = 1-2 sin² A + sin4 A. Substitute: 1+ sin A4 -cos4 A = 2 sin² A. The expression becomes: (2 sin² A) csc² A = 2 sin² A. (1 /sin2 A) = 2. Thus, the value is 2.
A man can swim downstream in 12 minutes covering a distance of 600 meters. He takes 15 minutes to cover the same distance upstream. Find the speed of th...
A boat covers 132 km downstream in 3 hours and 96 km upstream in 4 hours. The boat takes 8 hours to travel 'D' km upst...
A person rows 300 km against the current in 5 hours and travels 540 km along the current in 6 hours. How much time will he take to row 660 km in still w...
A boat can cover 140 km in downstream in 14 hours and 96 km in upstream in 12 hours. Find the distance travelled by the boat in still water in 5 hours.
A man’s speed with the current is 23 km/hr and the speed of the current is 6 km/hr . The man’s speed against the current is:
The speed of the stream is 14 km/h. Boat ‘A’ covers 130 km distance against the stream in 5 hours and boat ‘B’ covers 100 km distance against th...
A boat travels 48 km downstream in 3 hours and 36 km upstream in 3 hours. What is the speed of the stream (in km/h)?
Speed of a boat in still water is three times the speed of the boat in upstream. If the boat takes 25 minutes to cover 25 km in downstream, then find th...
A boat, whose speed in still water is 25% more than the speed of the current, covers 315 km downstream in _____ hours. The speed of the boat in still w...
A boy can swim in water with a speed of 13 km/hr in still water. If the speed of the stream is 5 km/hr, what will be the time taken by the boy to cover ...
Relevant for Exams:
