There exists a solution of θ between 0 and 2π that satisfies the equation .

a) True

b) False

The solution set of the equations  where x and y are real is ………….

a)

b)

c)

d) No solution

Fill in the blank
General values of θ satisfying the equation  are

a) θ = nπ

b)

c)

d) θ = nπ or θ =

The value of  is

a)

b)

c)

d) None of these

The principal value of is

a)

b)

c)

d)

e) None of these

If we consider only the principal values of the inverse trigonometric functions then the value of

 is

a)

b)

c)

d)

The number of solutions of  is

a) 0

b) One

c) Two

d) Infinite

The value of x for which  is

a)

b) 1

c) 0

d)

Find the value of  at  where
.

a) 1

b)

c)

d)

a) True

b) False

The numerical value of  is

a)

b)

c)

d)

In a triangle ABC, ∠ B = , ∠ C = . Let D divides BC internally in the ratio 1:3 then  is equal to

a)

b)

c)

d)

In a triangle ABC, is equal to

a)

b)

c)

d)

If the angles of a triangle are in the ratio 4:1:1 then the ratio of the longest side to the perimeter is

a)

b) 1 : 6

c)

d) 2 : 3

The sides of a triangle are in the ratio  then the angles of the triangle are in the ratio

a) 1 : 3 : 5

b) 2 : 3 : 4

c) 3 : 2 : 1

d) 1 : 2 : 3

Which one of the following is true in a triangle ABC?

a)

b)

c)

d)

One or more correct answers
In a triangle PQR, sin P, sin Q, sin R are in arithmetic progression then

a) Altitudes are in arithmetic progression

b) Altitudes are in harmonic progression

c) Medians are in geometric progression

d) Medians are in arithmetic progression

The external radii  of ΔABC are in harmonic progression then prove that a, b, c are in arithmetic progression

a) True

b) False

Let ABC be a triangle such that
 

If A, B, C are in arithmetic progression, determine the values of A, B, C.

a) 30°, 60°, 90°

b) 30°, 75°, 75°

c) 45°, 60°, 75°

d) 60°, 60°, 60°

Sum up to n terms and up to infinity
 

a)

b)

c)

d)

If   then

a)

b)

c)  or

d)  or

Let ABC be a triangle then prove that
tanA + tanB + tanC = tan A tanB tanC
cotA cotB + cotB cotC + cotC cotA = 1

The value of cos + cos + cos is

a) 0

b) 1

c)

d)