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Trigonometric Ratios and Identities

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  1. 1.Let A, B, where A,B (-( )/(2),( )/(2)), be the roots of the quadratic equation x^2-2x-5=0.
  2. 2.Let P= [0,4 ]: ^2 1 and S=a Z:2( ^8 - ^8 ) 2 =a^2, P.
  3. 3.If (( )/(18)) ((5 )/(18)) ((7 )/(18))=K, then the value of ((10K )/(3)) is:
  4. 4.If ( (A-B))/( A)+ ^2C ^2A=1,A,B,C (0,( )/(2)), then
  5. 5.The value of √3 20^ - 20^ 20^ 40^ 60^ 80^ is equal to
  6. 6.If x=(5)/(12) for some x ( ,(3 )/(2)), then 7x( (13x)/(2)+ (13x)/(2))+ 7x( (13x)/(2)- (13x…
  7. 7.Let ( )/(2)
  8. 8.The value of 10^ -√3 10^ is equal to :
  9. 9.If for [-( )/(3),0], the points (x,y)=(3 ( +( )/(3)),2 ( +( )/(6))) lie on xy+ x+ y+ =0, t…
  10. 10.If 10 ^4 +15 ^4 =6, then the value of 27 ^6 +8 ^6 16 ^8 is
  11. 11.If x+ ^2x=1, x (0,( )/(2)), then ( ^12x+ ^12x)+3( ^10x+ ^10x+ ^8x+ ^8x)+( ^6x+ ^6x) is equ…
  12. 12.If _r=1^131 (( )/(4)+(r-1)( )/(6)) (( )/(4)+(r )/(6))=a√3+b,a,b Z, then a^2+b^2 is equal t…
  13. 13.Let the range of the function f(x)=6+16 x (( )/(3)-x) (( )/(3)+x) 3x 6x,x R be [ , ].
  14. 14.The value of ( 70^ )( 10^ 70^ -1) is
  15. 15.If the value of [3 36^+5 18^5 36^-3 18^] is [a √5-bc], where a, b, c are natural numbers a…
  16. 16.If x=-(3)/(5), where <x<(3 )/(2), then 80( ^2x- x) is equal to
  17. 17.Suppose [0,( )/(4)] is a solution of 4 -3 =1.
  18. 18.If A=1x(x^2+x+1), B=xx^2+x+1 and C=(x^-3+x^-2+x^-1)^1/2,0<A,B,C<( )/(2), then A+B is equal…
  19. 19.The number of solutions, of the equation [e^ x-2 e^- x=2], is :
  20. 20.For , (0, /2), let 3 ( + )=2 ( - ) and a real number k be such that =k .
  21. 21.96 ( )/(33) (2 )/(33) (4 )/(33) (8 )/(33) (16 )/(33) is equal to :
  22. 22.The value of 36(4 ^29^ -1)(4 ^227^ -1)(4 ^281^ -1)(4 ^2243^ -1) is :
  23. 23.[ = 36^ ] is a root of which of the following equation?
  24. 24.[16 (20^ ) (40^ ) (80^ )] is equal to :
  25. 25.The value of 2sin (12[^]) - sin (72[^]) is :
  26. 26.The equation y = sinx sin (x + 2) -- sin2 (x + 1) represents a straight line lying in :
  27. 27.The value of sin 10^ sin30^ sin50^ sin70^ is :-
  28. 28.The value of cos210^ -- cos10^cos50^ + cos250^ is
  29. 29.If A= 3^ 9^ + 9^ 27^ + 27^ 81^ and B= 81^ - 3^ , then (B)/(A) is equal to ____ .
  30. 30.Let a_k=( _k)i+j and b_k=i-( _k)j, where _k=2^k-1 2^n+1, for some n N,n>5.
  31. 31.Let ( + )=-(1)/(10) and ( - )=(3)/(8), where 0< <( )/(3) and 0< <( )/(4).
  32. 32.Let the set of all a R such that the equation 2x+a x=2a-7 has a solution be [p,q] and r= 9…
  33. 33.The value of [ 9^- 27^- 63^+ 81^] is __________.
  34. 34.If the line x+4y=√7, where R, touches the ellipse 3x^2+4y^2=1 at the point P in the first …
  35. 35.Let the line y-x=1 intersect the ellipse x^22+y^2=1 at the points A and B.
  36. 36.If the points of intersection of the ellipses x^2+2y^2-6x-12y+23=0 and 4x^2+2y^2-20x-12y+3…
  37. 37.Let P(3, 2), 0, be a point on the ellipse x^29+y^24=1; let Q be a point on the circle x^2+…
  38. 38.Let H:x^2a^2-y^2b^2=1 be a hyperbola such that the distance between its foci is 6 and the …
  39. 39.Let the set of all values of r, for which the circles (x+1)^2+(y+4)^2=r^2 and x^2+y^2-4x-2…
  40. 40.Let the circle x^2+y^2=4 intersect the x-axis at the points A(a,0), a>0, and B(b,0).
  41. 41.Let a circle pass through the origin and its centre be the point of intersection of the tw…
  42. 42.Let the point P be the vertex of the parabola y=x^2-6x+12.
  43. 43.If P is a point on the circle S, Q is a point on a straight line L, and a given line M is …
  44. 44.Let E:x^2a^2+y^2b^2=1 (a>b) and H:x^2A^2-y^2B^2=1.
  45. 45.Let the product of the focal distances of the point (√3,12) on the ellipse x^2a^2+y^2b^2=1…
  46. 46.Let E:x^216+y^29=1.
  47. 47.Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be 2a…
  48. 48.Let P(4,3) be a point on a hyperbola H:x^2a^2-y^2b^2=1.
  49. 49.Let the shortest distance from the point (a,0), a>0, to the parabola y^2=4x be 4.
  50. 50.A line passing through the point (-2,0) touches the parabola y^2=x-2 at the point P in the…