As you want sample questions based on Trigonometry for preparation of IIT JEE Exam, so here I am providing following questions:

Trigonometry Sample Questions
If in triangle ABC, the altitudes from the vertices A, B, C on opposite sides are in
H.P., then sin A, sin B, sin C are in
( a ) G.P. ( b ) A.P. ( c ) Arithmetic-Geometric Progression ( d ) H.P. [ AIEEE 2005 ]

A person standing on the bank of a river observes that the angle of elevation of the
top of a tree on the opposite bank of a river is 60° and when he retires 40 m away
from the tree, the angle of elevation becomes 30°. The breadth of the river is
( a ) 20 m ( b ) 30 m ( c ) 40 m ( d ) 60 m [ AIEEE 2004 ]

If a, b, c are the sides of a triangle such that a : b : = : 3 : 2,
then A : B : C is
( a ) 3 : 2 : 1 ( b ) 3 : 1 : 2 ( c ) 1 : 3 : 2 ( d ) 1 : 2 : 3 [ IIT 2004 ]

Which of the following pieces of data does NOT uniquely determine an acute-angled
triangle ABC ( R being the radius of the circumcircle ) ?
( a ) a sin A, sin B ( b ) a, b, c ( c ) a, sin B, R ( d ) a, sin A, R [ IIT 2002 ]

The number of integral values of k for which the equation 7 cos x + 5 sin x = 2k + 1
has a solution is
( a ) 4 ( b ) 8 ( c ) 10 ( d ) 12 [ IIT 2002 ]

If f ( θ ) = sin θ ( sin θ + sin 3θ ), then f ( θ )
( a ) ≥ 0 only when θ ≥ 0 ( b ) ≤ 0 for all real θ
( c ) ≥ 0 for all real θ ( d ) ≤ 0 only when θ ≤ 0 [ IIT 2000 ]

A pole stands vertically inside a triangular park ∆ ABC. If the angle of elevation of
the top of the pole from each corner of the park is same, then in ∆ ABC, the foot of
the pole is at the
( a ) centroid ( b ) circumcentre ( c ) incentre ( d ) orthocentre [ IIT 2000 ]

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