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15%20-%20Trigonometry

# 15%20-%20Trigonometry - 15 TRIGONOMETRY Page 1 Answers at...

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15 - TRIGONOMETRY Page 1 ( Answers at the end of all questions ) ( 1 ) In triangle PQR, R = 2 π . If tan 2 P and tan 2 Q are the roots of the equation a x 2 + b x + c = 0, a 0, then ( a ) a = b + c ( b ) c = a + b ( c ) b = c ( d ) b = a + c [ AIEEE 2005 ] ( 2 ) In triangle ABC, let C = 2 π . If r is the inradius and R is the circumradius of the triangle ABC, then 2 ( r + R ) equals ( a ) b + c ( b ) a + b ( c ) a + b + c ( d ) c + a [ AIEEE 2005 ] ( 3 ) If cos - 1 x - cos - 1 2 y = α , then 4x 2 - 4xy cos α + y 2 is equal to ( a ) 2 sin 2 α ( b ) 4 ( c ) 4 sin 2 α ( d ) - 4 sin 2 α [ AIEEE 2005 ] ( 4 ) 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 ] ( 5 ) Let α , β be such that π < α - β < 3 π . If sin α + sin β = - 65 21 , then the value of cos 2 β α - is ( a ) - 130 3 ( b ) 130 3 ( c ) 65 6 ( d ) - 65 6 [ AIEEE 2004 ] ( 6 ) If u = sin θ + θ + θ + θ sin b sin a sin b cos a 2 2 2 2 2 2 2 2 , then difference between the maximum and minimum values of u 2 is given by ( a ) 2 ( a 2 + b 2 ) ( b ) 2 2 2 b a + ( c ) ( a + b ) 2 ( d ) ( a - b ) 2 [ AIEEE 2004 ] ( 7 ) The sides of a triangle are sin α , cos α and cos sin 1 α α + for some 0 < α < 2 π . Then the greatest angle of the triangle is ( a ) 60 ° ( b ) 90 ° ( c ) 120 ° ( d ) 150 ° [ AIEEE 2004 ]

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15 - TRIGONOMETRY Page 2 ( Answers at the end of all questions ) ( 8 ) 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 ] ( 9 ) If in a triangle a cos 2 2 C + c cos 2 2 A = 2 b 3 , then the sides a, b and c are ( a ) in A. P. ( b ) in G. P. ( c ) in H. P. ( d ) satisfy a + b = c [ AIEEE 2003 ] ( 10 ) The sum of the radii of inscribed and circumscribed circles, for an n sided regular polygon of side a, is ( a ) a cot π 2n ( b ) b cot  π n ( c ) π 2n cot 2 a ( d ) π 2n cot 4 a [ AIEEE 2003 ] ( 11 ) The upper 4 3 th portion of a vertical pole subtends an angle 5 3 tan 1 - at a point in the horizontal plane through its foot and at a distance 40 m from the foot. The height of the vertical pole is ( a ) 20 m ( b ) 40 m ( c ) 60 m ( d ) 80 m [ AIEEE 2003 ] ( 12 ) The value of cos 2 α + cos 2 ( α + 120 ° ) + cos 2 ( α - 120 ° ) is ( a ) 2 3 ( b ) 2 1 ( c ) 1 ( d ) 0 [ AIEEE 2003 ] ( 13 ) The trigonometric equation sin - 1 x = 2 sin - 1 a has a solution for ( a ) l a l < 2 1 ( b ) l a l 2 1 ( c ) 2 1 < l a l < 2 1 ( d ) all real values of
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15%20-%20Trigonometry - 15 TRIGONOMETRY Page 1 Answers at...

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