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)

sin10° sin50° sin70°=

a)

b)

c)

d)

Evaluate

a)

b)

c)

d)

Prove that area of a triangle is

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