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Trigonometric Functions and Equations

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  1. 1.The number of values of x in the interval [[ 0,3 ],] satisfying the equation [2 ^2x + 5 x …
  2. 2.The number of x [ ] [0, 2[ ] ] for which [| 2 ^4x + 18 ^2x - 2 ^4x + 18 ^2x | = 1] is :
  3. 3.If sum of all the solutions of the equation [8 x.( ( 6 + x ). ( 6 - x ) - 1 2 ) = 1] in [0…
  4. 4.The number of solutions of sin3x = cos 2x, in the interval [( 2, )] is :
  5. 5.The sum of all values of [ ] [ ] ( 0, 2 ) ( satisfying sin2 2] + cos4 2 =3 4
  6. 6.If [x] denotes the greatest integer [ ] x, then the system of linear equations [sin [ ]]x …
  7. 7.Let S be the set of all [ ] [ ] R such that the equation, cos2x + [ ]sinx = 2[ ]-- 7 has a…
  8. 8.The number of solutions of the equation 1 + sin4 x = cos23x, [x [ - 5 2,5 2 ]] is :
  9. 9.Let S = [ ] [ ] [--2[ ], 2[ ]] : 2cos2[ ] + 3sin[ ] = 0.
  10. 10.If 0 [ ] x < [ 2], then the number of values of x for which sin x - sin 2x + sin 3x = 0, i…
  11. 11.The number of roots of the equation, (81)sin2x + (81)cos2x = 30 in the interval [ 0, [] ] …
  12. 12.The number of solutions of the equation x + 2tanx = [ 2] in the interval [0, 2[]] is :
  13. 13.The number of solutions of sin7x + cos7x = 1, x[] [0, 4[]] is equal to
  14. 14.All possible values of [] [] [0, 2[]] for which sin 2[] + tan 2[] > 0 lie in :
  15. 15.The sum of all values of x in [0, 2[]], for which sin x + sin 2x + sin 3x + sin 4x = 0, is…
  16. 16.The sum of solutions of the equation [ x 1 + x = | 2x |], [x ( - 2, 2 ) - 4, - 4 ] is :
  17. 17.The number of solutions of the equation [32^ ^2x + 32^ ^2x = 81,,0 x 4] is :
  18. 18.The number of solutions of the equation [ ( x + 3 ) ( 3 - x ) = 1 4 ^22x], [x [ - 3 ,3 ]] …
  19. 19.Let [S= [0,2 ]: 8^2 ^2 +8^2 ^2 =16 .] Then [n(s) + _ S^ ( ( 4 + 2 ) ec( 4 + 2 ) ) ] is equ…
  20. 20.Let for some real numbers [] and [], [a = - i ].
  21. 21.The number of elements in the set [S=x R: 2 (x^2+x6)=4^x+4^-x] is :
  22. 22.Let [S=x (-()/(2), ()/(2)): 9^1- ^2 x+9^ ^2 x=10] and [=_x S ^2((x)/(3))], then [(1)/(6)(-…
  23. 23.The number of solutions of the equation 4 ^2 x-4 ^3 x+9-4 x=0 ; x [-2 , 2 ] is :
  24. 24.If [2 ^2 -5 =1] has exactly 7 solutions in the interval [[0, (n )/(2)]], for the least val…
  25. 25.The sum of the solutions [x R] of the equation [(3 2 x+ ^3 2 x)/( ^6 x- ^6 x)=x^3-x^2+6] i…
  26. 26.If [2 ^3 x+ 2 x x+4 x-4=0] has exactly 3 solutions in the interval [[0, n 2], n N], then t…
  27. 27.Let [| (60-) (60+)| (1)/(8), [0,2 ]].
  28. 28.The sum of all values of [0,2 ] satisfying 2 ^2 = 2 and 2 ^2 =3 is
  29. 29.If [-(7 )/(6), (4 )/(3)], then the number of solutions of √3 cosec^2 -2(√3-1) cosec -4=0, …
  30. 30.If [-2 , 2 ], then the number of solutions of 2 √2 ^2 +(2-√6) -√3=0, is equal to:
  31. 31.The number of solutions of the equation (4-√3) x-2 √3 ^2 x=-41+√3, x [-2 , (5 )/(2)] is
  32. 32.[ The number of solutions of the equation 2 x+3 x=, x [-2 , 2 ]- ()/(2), (3 )/(2) is: ]
  33. 33.The number of solutions of the equation 2 ()/(2) + (5)/(2) = 2^3 (5)/(2) in [ -()/(2), ()/…