Solve the equation

2sin4x + 16sin³xcosx + 3cos2x – 5 = 0

a) sinx

b) cosx

c) sin2x

d) cos2x

a)

b) 2 (1 – cot 22°)

c)

d) 2 (1 – cot 22°)

tan3a – tan2a – tana =

a) tan3a tan2a tana

b)

c)

d)

Evaluate
cos36° − cos72°

a)

b)

c)

d)

Evaluate

a)

b)

c)

d)

Prove that area of a triangle is

The lengths of the two sides of a triangle are 1 unit and  units respectively and the angle opposite the shorter side is 30. Prove that there are two triangles satisfying these conditions. Find their angles and show that their areas are in the ratio  

In any triangle prove that

In a triangle ABC if cot A, cot B, cot C are in arithmetic progression then  are in .  .  .  .  . progression

a) arithmetic

b) geometric

c) harmonic

d) neither of the above

In a triangle ABC,   then the value of angle A in degrees is

a) 45°

b) 60°

c) 75°

d) 90°

In ΔABC, AD is an altitude from A. Given b > c, ∠C = 23 and
AD = then ∠B is equal to

a) 90°

b) 102°

c) 107°

d) 113°

In a triangle ABC, a : b : c = 4 : 5 : 6. The ratio of the radius of the circumcircle to the incircle is

a) 15:7

b) 16:7

c) 2

d) 17:7

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

a) a unique solution

b) infinite number of solutions

c) no solutions

d) none of the above

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

a)

b)

c)

d)

 is equal to

a)

b)

c)

d)

AB is a vertical pole and C is the midpoint. The end A is on the level ground and P is any point on the level ground other than A. The portion CB subtends an angle β at P. If AP : AB = 2 : 1 then β is equal to

a)

b)

c)

d)

In the interval  the equation (cos2x) = 2 has

a) no solution

b) unique solution

c) two solutions

d) infinitely many solutions

The value of  is

a) 0

b) 1

c)

d)

Let α, β be any two positive values of x for which 2cosx, |cosx| and 1 – 3cos²x are in geometric progression. The minimum value of |α–β| is

a)

b)

c)

d) None of these

If sinθ +sin²θ = 1, then the value of
cos¹⁰θ + 3cos¹⁰θ + 3cos⁸θ + cos⁶θ – 1 is equal to

a) 2

b) 1

c) –1

d) 0

The number of real solutions of  is

a) Zero

b) One

c) Two

d) Infinite

If in a ΔABC, ∠A = , ∠B =  then ∠C is equal to

a)

b)

c)

d) None of these