Question

The equation cos 2x + a sin x = 2a – 7 possesses a solution if

Solution

Correct option is

2 ≤ a ≤ 6

The given equation can be written as

 1 – 2 sin2 x + a sin x = 2a – 7

 ⇒ 2sin2 x – a sin x + 2 a – 8 = 0

 

Hence, sin x = (a – 4)/2( the other value is not possible as . This value is possible only when

   

 

SIMILAR QUESTIONS

Q1

If A lies in the second quadrant and 3 tan A + 4 = 0, the value of 2 cot A – 5 cos A + sin A is equal to

Q2

The value of the determinant

                          

Is zero if

Q3

  is equal to

Q4

An angle α is divided into two parts so that the ratio of the tangents of these parts is λ. If the difference between these parts is x then sinx/sinα is equal to

Q5

 

 or equal to

Q6

Given θ Ïµ (0,π/4) and t1 = (tan θ)tanθ t2 = (tan θ)cotθt3 = (cot θ)tanθand t4 = (cot θ)cotθ then

Q7

If x = sin αy = sin βz = sin (α + β) then cos (α + β) =

Q8

The radius of the circle

 

Q9

If tan x + tan (x + π/3) + tan (x + 2π/3) = 3, then

Q10

sin 470 + sin 610 – sin 110 – sin 250 is equal to