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
Your Answer
Solve the equation
2sin4x + 16sin3xcosx + 3cos2x – 5 = 0
a) sinx
b) cosx
c) sin2x
d) cos2x
b) 2 (1 – cot 22°)
d) 2 (1 – cot 22°)
tan3a – tan2a – tana =
a) tan3a tan2a tana
d)
Evaluate cos36° − cos72°
sin10° sin50° sin70°=
Evaluate
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
is equal to
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
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
If sinθ +sin2θ = 1, then the value of cos10θ + 3cos10θ + 3cos8θ + cos6θ – 1 is equal to
a) 2
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
