Trigonometry for IIT JEE

Trigonometry for IIT JEE – 2013 2013

Q1. If

1  1 2 ......

tan  1

 n

 2

 prove that

sin 1 sin  2 ...... sin  n

 tan n

cos 1 cos  2 ...... cos n

Q2. Find all values of   lying between

0

{

 and 2  , satisfying the

r sin =  3 . r 4sin = 2   3 1 

equations

{

Q3. Let  A= {  :2cos2  sin  2 }  and  B =  :

Q4. Find all the values of   in



−   , 2

2



 }

 3    2 2

. Find  A ∩ B .

 which satisfy the equation

 1− tan   1 sin2 =1  tan  . Q5. Find the value of  x   in − ,   which satisfy the equation 1 ∣cos x ∣∣cos  x ∣∣cos  x ∣ . ..... ∞ 8 = 43 . 2

3

Q6. Solve for real  x   and  y  : Q7. If

−1

cos

cot

2

 x  y  tan2  x  y  y 2 2 y − 1= 0 .

p  p2 q2 2 p q −1 q 2 cos =  then show that  − cos = sin  . a b a2 b2 a b

Q8. Solve for  x  : sin [ cos−1 cot  2tan−1 x  ]=0 − − Q9. Find the value of cot 9  cosec 1

1

41  41 4

.

Q10. Shade the region in the  x y   plane corresponding to the truth set:  x  0 , y  0 , x 2− 2 y  y 2 0 , y  sec x  .

Dr. Dr. Rajiv K. Sharda

Trigonometry rigonometr y for IIT JEE 2013

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Q11. Find the coordinates of the points of intersection of the curves    y = cot x   and  y = sin3 x   if −  x  . 2

2

Q12. Three circles touch one another externally. The tangents at their points of contact meet at a point whose distance from a point of contact is 4. Find the ratio of the product of the radii to the sum of the radii of the circles.

Let O  be a point inside a  ABC  , such that ∢ OAB=∢OBC =∢ OCA=  then show that cot = cot A  cot B cot C  . (II). Also prove that cosec 2 = cosec 2 A cosec 2 B cosec 2 C  .

Q13. (I).

Q14. If the bisector of angle  A  of  ABC   meets the opposite side in  D , A 2bc cos prove that  AD = . 2 b c

1

Q15. In a  ABC  , the median of the side  BC   is of length

and it divides the angle  A  into angles of length of the side  BC  .

0

30

 and

 11− 6  3 0

45

. Find the

Q16. In a  ABC   having sides a , b , c , if C =600  prove that 1

ac



1

b c

=

3

a b  c

.

Q17. Find the greatest angle of the triangle whose sides are  x 2  x 1 , 2 x 1 and  x 2 −1 .

 

0

1 Q18. Show that tan 88 =  3 2  2 1  2 Q19. Prove that : cos

2 3 7 1  ×cos × cos × ......× cos = 7 15 15 15 15 2

Q20. Prove that: cos2 = 2sin 2  4cos  sin  sin  cos2 

Dr. Rajiv K. Sharda

Trigonometry for IIT JEE 2013

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Q21. IIT JEE 2011 Let  P ={  :sin −cos =  2cos  }  and Q = {  :sin  cos =  2 sin  }  be two sets . Then (A). P ⊂Q  and Q − P ≠ (B). Q⊄ P (C). P ⊄Q (D). P =Q Q22. IIT JEE 2011 The positive integer value of n 3  satisfying the 1 1 1 =  equation sin  2 3   is ______. sin sin n n n

      

∣

1

tan 

Q23. IIT JEE 2011 If  f = −tan    1 −1 −tan    f   : 0   is ______. 2

{

1

∣

tan  1

 then the set

}

Q24. The number of all possible values of   where 0  , for which the system of equations

 y  z  cos3 = x y z  sin3  2cos3  2sin3    x sin 3 =  y   z  x y z  sin3 =  y  2 z  cos3  y sin3  have a solution

 x   , y   , z  0

0

0

 with  y 0 , z 0≠ 0  is ______.

Q25. The minimum value of the expression

1 sin

2

 3sin  cos 5 cos2 

 is

______.

Dr. Rajiv K. Sharda

Trigonometry for IIT JEE 2013

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