Q.1 Find the value of :- (log sin 1° + log sin 2° ………..+ log sin 89°) + (log tan 1° + log tan 2° + ……… + log tan 89°) - (log cos 1° + log cos 2° + ……… + log cos 89°)

Q.2 Ram and Shyam are 10 km apart. They both see a hot air balloon passing in the sky making an angle of 60° and 30° respectively. What is the height at which the balloon could be flying?

Q.3 A man standing on top of a tower sees a car coming towards the tower. If it takes 20 minutes for the angle of depression to change from 30° to 60°, what is the time remaining for the car to reach the tower?

Q.4 A right angled triangle has a height ‘p’, base ‘b’ and hypotenuse ‘h’. Which of the following value can h2 not take, given that p and b are positive integers?

Q.5 If tan? + sin? = m, tan? − sin? = n, Find the value of m² - n ²

Q.6 A student is standing with a banner at the top of a 100 m high college building. From a point on the ground, the angle of elevation of the top of the student is 60° and from the same point, the angle of elevation of the top of the tower is 45°. Find the height of the student.

Q.7 If Cos x – Sin x = ?2 Sin x, find the value of Cos x + Sin x:

Q.8 If (2sinx)/(1+cosx+sinx) = t, (1-cosx+sinx)/(1+sinx) can be written as:

Q.9 A tall tree AB and a building CD are standing opposite to each other. A portion of the tree breaks off and falls on top of the building making an angle of 30°. After a while it falls again to the ground in front of the building, 4 m away from foot of the building, making an angle of 45°. The height of the building is 6 m. Find the total height of the tree in meters before it broke.

Q.10 A flag is hoisted on top of a building of height 7?3 m. A man of height ?3 m, standing on the ground, sees the top and bottom of the flag pole at 2 different angles of elevation that are found to be complementary. If the man is standing ?135 m away from the building, find the height of the flag pole