### Eamcet - Maths - Trigonometric Ratios And Identities

A+B= C⇒cos2A +cos2B + cos2C - 2 cos A cos B cos C

A.  1

B.  2

C.  0

D.  3

If (tan 3A / tan A) =α then ( sin 3A/ sin A) =

A.  2a/a+1

B.  2a/a-1

C.  a/a+1

D.  a/a-1

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

A.  {1,0}

B.  {-1,1}

C.  {0,1/2}

D.  {2,0}

In a ∆ ABC, (a-b)2cos2(C/2)+(a+b)2sin2(C/2) is equal to

A.  a2

B.  c2

C.  b2

D.  a2+b2

If  cos θ - 4 sin θ = 1 then  sin θ + 4 cos θ   is equal to

A.  ±1

B.  0

C.  ±2

D.  ±4

The expression tan 90– tan 270– tan 630is equal to :

A.  4

B.  3

C.  2

D.  1

In a ΔABC, cos[(B+2C+3A)/2]+cos[(A-B)/2] is equal to

A.  -1

B.  0

C.  1

D.  2

The angle between the lines represented by y2sin2θ-xysin2θ+x2(cos2θ-1)=0 is

A.  π/3

B.  π/4

C.  π/6

D.  π/2

The number of natural numbers less than 1000, in which no two digits are repeated, is :

A.  738

B.  792

C.  837

D.  720

In ΔABC, 1+4 sin(π-A/4)sin(π-B/4)sin(π-C/4)=

A.  sin A/2+ sin B/2+ sin C/2

B.  cos A/2+ cos B/2+ cos C/2

C.  sin A/2+ sin B/2- sin C/2

D.  cos A/2+ cos B/2- cos C/2

Log3√2324 =

A.  4

B.  6

C.  8

D.  3

1- cos A+ cos B- cos (A+B)/1+cos A- cos B- cos(A+B)=

A.  sin A/2. Cos B/2

B.  tan A/2.cot B/2

C.  sec A/2.cosec B/2

D.  none

(sin θ+ cosec θ)2+(cos θ+ sec θ)2 =

A.  tan2 θ+ cot2 θ+7

B.  sin2 θ+ cos2 θ+7

C.  sec2 θ+ cosec2 θ+7

D.  cos2 θ+ cot2 θ+7

If sin α+ sin β= a, cos α+ cos β = b then sin(α+β)=

A.  2ab/a2+b2

B.  ab/a2+b2

C.  a2+b2/2ab

D.  b2 -a2/ b2 +a2

In ΔABC , cos(A+2B+3C/2)+cos(A-C/2) =

A.  0

B.  1

C.  -1

D.  2

If A+B+C= 2S, then cos2 S+ cos2 (S-A)+ cos2 (S-B)+ cos2 (S-C)=

A.  2 sin A cos B sin C

B.  4 cos A/2 cos B/2 cos C/2

C.  2+ 2 cos A cos B cos C

D.  sin A sin B

If A+B+C=1800 then cos 3A+cos 3B+cos 3C=

A.  4 cos 3A/2 cos 3B/2 cos 3C/2

B.  - 4 cos 3A/2 cos 3B/2 cos 3C/2

C.  1- 4 cos 3A/2 cos 3B/2 cos 3C/2

D.  1-4 sin 3A/2 sin 3B/2 sin 3C/2

The point on the line 3x+4y = 5 which is equidistant from (1,2) and (3,4) is

A.  (7,-4)

B.  (15,-10)

C.  (1/7 , 8/7)

D.  (0 , 5/4)

If X follows a binomial distribution with parameters n = 6 and p. If 4P(X = 4) = P(X = 2), then p is equal to

A.  1 / 2

B.  1 / 4

C.  1 / 6

D.  1 / 3

If log2(sin x)- log2(cos x)- log2(1-tan x)- log2(1+tan  x)= -1 then tan 2x=

A.  -1

B.  1

C.  1/2

D.  4

In ΔABC,   tan (A/2)tan (B/2)+ tan (B/2)tan (C/2)+ tan (C/2) tan (A/2)=

A.  0

B.  1

C.  -1

D.  2

If k=(1+sin A)(1+sinB)(1+sin C)=(1-sinA)(1-sin B)(1-sin C) then k=

A.  ± sin Asin Bsin C

B.  ± cos A cos B cos C

C.  1

D.  0

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

A.  2

B.  3

C.  4

D.  5

If x cos α= y cos(2π/3+ α)= z cos(4π/3+ α),then xy+yz+zx=

A.  0

B.  1

C.  -1

D.  2

If cos θ= 3/5 and θ is not in the first quadrant,then (5tan(π+ θ)+4 cos(π- θ))/(5sec(2π-θ)- 4 cot(2π+θ) )

A.  4/5

B.  -4/5

C.  5/4

D.  -5/4

The range of 5 Co-1(3x) is

A.  [0, 5π]

B.  [-3, 3]

C.  [-1, 1]

D.  [0, π]

The point (3, 2) undergoes the following three transformations in the order given i) Reflection about the line y = x ii) Translation by the distance 1 unit in the positive direction of x – axis iii) Rotation by an angle π/4 about the origin in the anticlockwise direction. Then the final position of the point is

A.  (-√18,√18)

B.  (-2, 3)

C.  (0,√18)

D.  (0,3)

(cos 2α /cos4α- sin4 α)- (cos4 α+ sin4 α/ 2- sin22α)=

A.  0

B.  1

C.  1/2

D.  2

Find the equation of the parabola, whose axis parallel to the y-axis and which passes through the points (0,4),(1,9) and (4,5) is

A.  Y=-x2+x+4

B.  Y=-x2+x+1

C.  Y=(-19x2/12)+(79x/12)+4

D.  Y=(-19x2/12)+(89/12)+1

The value of (i)i is equal to

A.  ω

B.  ω2

C.  π/3

D.  none of these