The Value Of The Determinant                            Is Zero If

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Question

The value of the determinant

                          

Is zero if

Solution

Correct option is

sin x = 0

Appling C1 → C1 + C3 – 2cos x C2, the given determinant is equal to

                     

                                                                                                               

                     

                     

Which is zero if sin x = 0 or cos x = (1+a2)/2a. As a ≠ 1,  

                           (1 + a2)/2a >1

Therefore, cos x = (1+ a2)/2a is not possible.

Testing

SIMILAR QUESTIONS

Q1

If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then aband c satisfy the relation

Q2

If sin x + sin2 x = 1, then the value of cos12 x + 3 cos10 x + 3 cos8 x + cos6 x – 1 is equal to

Q3

The value of

      

Q4

If θ lies in the first quadrant and cos θ = 8/17, then the value of cos (300 +θ) + cos (450 – θ) + cos (1200 – θ) is

Q5

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

Q6

  is equal to

Q7

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

Q8

 

 or equal to

Q9

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

Q10

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