CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Evaluation of a Determinant

If cosec α 1...

Question

If $∣ ∣ ∣ ∣ \begin{matrix} cosec α & 1 & 0 1 & 2 cosec α & 1 0 & 1 & 2 cosec α \end{matrix} ∣ ∣ ∣ ∣ = λ {cosec}^{3} α - μ cosec α,$
then the value of $λ + μ$ is

Open in App

Solution

$L H S = ∣ ∣ ∣ ∣ \begin{matrix} cosec α & 1 & 0 1 & 2 cosec α & 1 0 & 1 & 2 cosec α \end{matrix} ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ \begin{matrix} cosec α & 1 & 0 0 & 2 cosec α - sin α & 1 0 & 1 & 2 cosec α \end{matrix} ∣ ∣ ∣ ∣ [R_{2} \to R_{2} - sin α R_{1}] = 4 {cosec}^{3} α - 3 cosec α \Rightarrow λ + μ = 7$

Suggest Corrections

thumbs-up

2

Similar questions

α, β

are the roots of the equation

x^{2} - 4 x + λ = 0

γ, δ

are the roots of the equation

x^{2} - 64 x + μ = 0

α, β, γ, δ

forms an increasing G.P., then the value of

\frac{μ}{λ}

Q. If perimeters of

△ L M N

△ A B C

λ

μ

, then the value of

\frac{λ}{μ}

s e c α = \frac{2}{\sqrt{3}}

then find the value of

\frac{1 - c o s e c α}{1 + c o s e c α}

α

is in IV quadrant.

Q. If perimeter of

△ L M N

△ A B C

λ

μ

\frac{λ}{μ}

Q. If the equations

4 x^{2} - x - 1 = 0

3 x^{2} + (λ + μ) x + λ - μ = 0

have a root common then the rational values of

λ

μ

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Evaluation of a Determinant

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon