Eamcet - Maths - Trigonometric Ratios And Identities Test

Test Instructions :

1. The Test is 1hr duration.
2. The Test Paper consists of 30 questions. The maximum marks are 30.
3. All the questions are multiple choice question type with three options for each question.
4. Out of the three options given for each question, only one option is the correct answer.
5. Each question is allotted 1 mark for each correct response.
6. 0.25 will be deducted for incorrect response of each question.
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If α,β,γ are the roots of the equation x3+px2+qx+r = 0 then the coefficient of x in the cubic equation whose roots are α(β+γ), β(γ+α) and γ(α+β) is

  

  

  

  

If sin θ+ cos θ=a then sin4 θ+ cos 4 θ=

  

  

  

  

The equation of the sphere through the points (1,0,0) (0,1,0) and (1,1,1) and having the smallest radius

  

  

  

  

cos 60 sin 240cos 720 is equal to

  

  

  

  

If A+B+C= 1800 then sin3 A cos (B-C)+ sin3 B cos (C-A)+ sin3 C cos (A-B)=

  

  

  

  

tan x + tan(x + π/3)+tan(x+2π/3)=3⇒tan3x=

  

  

  

  

tan 5850. cot 4050+ tan6750 cot 7650=

  

  

  

  

If A+B+C= 1800 then cos 2A+ cos 2B+ cos 2C+1=

  

  

  

  

If cos x= tan y, cos y= tan z, cos z=tan x then

  

  

  

  

(cos A+ cos 3A+cos 5A+cos 7A)/ (sin A+sin 3A+sin 5A+sin 7A)=

  

  

  

  

(tan 230+ tan220)/(1- tan 230 .tan220)=

  

  

  

  

If x = sint; y = sin pt then (1-x2) (d2y/dx2) -x(dy/dx) +p2y =

  

  

  

  

P(-1, -3) is a centre of similitude for the two circles x2+y2=1 and x2+y2-2x-6y+6=0. The length of the common tangent through P to the circle is

  

  

  

  

cos π/11 cos 2π/11 cos 3π/11 cos 4π/11 cos 5π/11=

  

  

  

  

cos A+sin(2700+A)-sin(2700-A)+cos(1800-A)=

  

  

  

  

The extreme values of cos x cos ((2π/3)+x) cos ((2π/3)-x) is

  

  

  

  

tan α+ 2 tan α+ 4 tan 4α+ 8 cot 8α =

  

  

  

  

sec4 θ (1- sin4θ) - tan2θ=

  

  

  

  

1+(1+2)/2!+(1+2+22)/3!+(1+2+22+23)/4!+ ....... =

  

  

  

  

(cos 6x+ 6 cos 4x+15 cos 2x+10)/( cos 5x+5 cos 3x+10 cos x)=

  

  

  

  

The value of sin θ / ( sin2(π/8+ θ/2)- sin2(π/8-θ/2)) =

  

  

  

  

If sin-1x+sin-1(1-x)=cos-1x, then x ε to

  

  

  

  

The distance between the parallel lines given by (x + 7y)2+4√2(x+7y)-42=0 is

  

  

  

  

2 cos θ-cos 3θ- cos 5θ- 16 cos3θsin2 θ=

  

  

  

  

sin 3θ/2 cot θ/2 cosθ=

  

  

  

  

The value of k such that the lines 2x -3y + k = 0,3x - 4y - 13=0 and 8x - 11y -33 = 0are concurrent, is

  

  

  

  

If x=2/(3+√7),then (x-3)2 is equal to

  

  

  

  

cos2 10+cos2 20+ cos2 30+.... cos2 900 =

  

  

  

  

If Sin6θ + Cos6θ + Kcos2θ=1 then k=

  

  

  

  

If cot θ=-3/4 and θ is not in the second quadrant then 5 sin θ+10 cos θ+9 sec θ-16 cosecθ- 4cot θ=

  

  

  

  

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