Home
Class 12
MATHS
|(sin alpha, cosalpha,sin(alpha+delta)),...

`|(sin alpha, cosalpha,sin(alpha+delta)),(sinbeta, cos beta,sin(beta+delta)),(singamma,cosgamma,sin(gamma+delta))|=`

A

0

B

1

C

`1+sinalphasinbetasingamma`

D

`1-(sinalpha-sinbeta)(sinbeta-singamma)(singamma-sinalpha)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Similar Questions

Explore conceptually related problems

If /_\ = |[sinalpha, cosalpha, sin(alpha+delta)],[sinbeta, cosbeta, sin(beta+delta)],[singamma, cosgamma, sin(gamma+delta)]| then prove that /_\ is independent of alpha, beta, gamma and delta.

Without expanding evaluate the determinant det[[sin alpha,cos alpha sin(alpha+delta)sin beta,cos beta,sin(beta+delta)sin gamma,cos gamma,sin(gamma+delta)]]

Without expanding evaluate the determinant |sin alpha cos alpha sin(alpha+delta)sin beta cos beta sin(beta+delta)sin gamma cos gamma sin(gamma+delta)|

Prove that det [[sin alpha, cos alpha, sin (alpha + delta) sin beta, cos beta, sin (beta + delta) sin gamma, cos gamma, sin (gamma + delta)]] = 0

Show that |[sinalpha, cosalpha, cos(alpha+delta)],[sinbeta, cosbeta, cos(beta+delta)],[singamma, cosgamma, cos(gamma+delta)]|=0

Without expanding,show that the value of each of the determinants is zero: det[[sin alpha,cos alpha,cos(alpha+delta)sin beta,cos beta,cos(beta+delta)sin gamma,cos gamma,cos(gamma+delta)]]

sin alpha, cos alpha, cos (alpha + delta) sin beta, cos beta, cos (beta + delta) sin gamma, cos gamma, cos (gamma + delta)] | = 0

If Delta=|(sin alpha, cos alpha, sin alpha+cos beta),(sin beta, cos alpha, sin beta+cos beta),(sin gamma, cos alpha, sin gamma+cos beta)| then Delta equals

Show that the determinant Delta (x) is given by Delta (x) = |{:(sin(x+alpha),cos(x+alpha),a+xsinalpha),(sin(x+beta),cos(x+beta),b+xsinbeta),(sin(x+gamma),cos(x+gamma),c+xsingamma):}| is independent of x.

If Delta = det [[sin alpha, cos alpha, sin alpha + cos alphasin beta, cos alpha, sin beta + cos betasin gamma, cos alpha, sin gamma + cos beta]] then Delta