If in a triangle ABC, the altitude from the vertices A, B, C on opposite sides are in harmonic progression, then sin A, sin B, sin C are in

a) Harmonic Progression

b) Arithmetico – Geometric Progression

c) Arithmetical Progression

d) Geometric Progression

Let α, β be such that π < α – β < 3π. If sin α + sin β =  and cos α + cos β =   then the value of cos  is

a)

b)

c)

d)

The sides of a triangle are sinα, cosα and   for some 0 < α <  then the greatest angle of the triangle is

a) 60°

b) 90°

c) 120°

d) 150°

A person standing on the bank of a river observes the angle of elevation of the top of the tree on the opposite bank of the river is 60° and when he retires 40 m away from the tree the angle of elevation becomes 30°. The breadth of the river is

a) 20m

b) 30m

c) 40m

d) 60m

If f : R  Ś̨, defined by f(x) = sin x   cos x + 1, is onto then the interval of Ś̨  is

a) [ 0, 3 ]

b) [-1, 1 ]

c) [0, 1 ]

d) [-1, 3]

In a triangle ABC, a cos²  + c cos²  =   then the sides a, b, c are in

a) Arithmetic Progression

b) Geometric Progression

c) Harmonic  Progression

d) Satisfy a+ b = c

The trigonometric equation sin^-1x = 2sin^-1α has a solution for

a)  < |α | <  

b) All real values of α

c) |α | ≤

d) |α | ≥

cot^-1() – tan^-1 () = x then sin x is equal to

a) tan²

b) cot²

c) tanα

d) cot

In a triangle ABC, 2ca sin  is equal to

a) a² + b² – c²

b) c² + a² – b²

c) b² – c² – a²  

d) c² – a² – b²

sin²θ =  is true if and only if

a) x – y ≠ 0

b) x = y

c) x ≠ .y

d) x ≠ 0, y ≠ 0

The value of   is

a) 1

b)

c)

d) 2

If sin (α + β) = 1, sin (α  β) =  , then tan (α + 2β) tan (2α + β) is equal to

a) 1

b) 1

c) Zero

d) None of these

If y = sin²θ + cosec²θ, θ ≠ 0 then

a) y = 0

b) y ≤ 2

c) y ≥ 2

d) y ≥ 2

In a triangle ABC, a= 4, b =3, angle A = 60° then c is a root of the equation

a) c²  3c  7 = 0

b) c² + 3c + 7 = 0

c) c²  3c + 7 = 0

d) c² + 3c  7 = 0

In a triangle tan  = , tan  =  , then

a) a, c, b are in Arithmetic Progression

b) a, b, c are in Arithmetic Progression

c) b, a, c are in Arithmetic Progression

d) a, b, c are in Geometric Progression

If α is a root of 25cos²θ + 5cosθ  12 = 0,  < α < π then sin2α is equal to

a)

b)

c)

d)

tan^-1  + tan^-1 is equal to

a)  cos^-1   

b)  sin^-1   

c)  tan^-1   

d) tan^-1

The equation   a sin x + b cos x = c   where |c| >  has

a) a unique solution

b) infinite number of solutions

c) no solution

d) none of these

The angles of a triangle are in Arithmetic Progression and let . Find the angle A.

Root(s) of the equation 2sin²θ + sin²2θ = 2

Let P =  and
 be two sets then

a) P⊂Q and Q – P = ϕ

b) Q  P

c) P  Q

d) P = Q

The positive integer satisfying the equation
  is

The value of x satisfying tan⁻¹  (x + 3) − tan⁻¹ (x – 3) = sin⁻¹ are