prove that\(\left( \frac { co{ s }^{ 3 }A-si{ n }^{ 3 }A }{ cosA-sinA } \right) -\left( \frac { co{ s }^{ 3 }A+si{ n }^{ 3 }A }{ cosA+sinA } \right) =2sinAcosA\)

prove that \(\frac { sinA }{ secA+tanA-1 } +\frac { cosA }{ cosecA+cotA-1 } =1\)

As observed from the top of a 60 m high light house from the sea level, the angles of depression of two ships are 28° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (tan28° = 0.5317)

A man is watching a boat speeding away from the top of a tower. The boat makes an angle of depression of 60° with the man’s eye when at a distance of 200 m from the tower. After 10 seconds, the angle of depression becomes 45°. What is the approximate speed of the boat (in km / hr), assuming that it is sailing in still water ?(\(\sqrt { 3 } \) = 1.732)