Home
Class 12
MATHS
If f(alpha,beta)=|(cos alpha,-sin alpha,...

If `f(alpha,beta)=|(cos alpha,-sin alpha,1),(sin alpha,cos alpha,1),(cos(alpha+beta),-sin(alpha+beta),1)|,`then

A

f(300,200=f(400,200)

B

f(200,400)=f(200,600)

C

f(100,200)=f(200,200)

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A, C
`|{:(cos alpha,,-sin alpha,,1),(sin alpha,,cos alpha,,1),(cos (alpha+beta),,-sin(alpha+beta),,1):}|`
`=|{:(cos alpha,,-sinalpha,,1),(sin alpha,,coa alpha,,1),(0,,0,,1+ sin beta -cos beta):}|`
`"[Applying " R_(3) toR_(3)-R_(1) (cos beta) +R_(2) (sin beta)"]"`
`=(1+sin beta -cos beta) (cos^(2) alpha+ sin^(2)alpha)`
`=1+ sin beta- cos beta `which is independent of `alpha`
Promotional Banner

Similar Questions

Explore conceptually related problems

cos alpha,-sin alpha,1sin alpha,cos alpha,1cos(alpha+beta),-sin(alpha+beta),1]|

cos alpha,-sin alpha,1sin alpha,cos alpha,1cos(alpha+beta),-sin(alpha+beta),1]|

If Delta = |(cos alpha,- sin alpha,1),(sin alpha,cos alpha,1),(cos (alpha + beta),- sin (alpha + beta),1)| , then

If A(alpha, beta)=[("cos" alpha,sin alpha,0),(-sin alpha,cos alpha,0),(0,0,e^(beta))] , then A(alpha, beta)^(-1) is equal to

The value of the determinant ,cos alpha,-sin alpha,1sin alpha,cos alpha,1cos(alpha+beta),-sin(alpha+beta),1]| is equal

If A(alpha)=[[cos alpha,sin alpha],[-sin alpha,cos alpha]] then A(alpha)A(beta)

A_((alpha))=[{:(cos alpha,-sin alpha),(sin alpha,cos alpha):}],A_((beta))=[{:(cos beta,-sin beta),(sin beta,cos beta):}] Which one of the following is correct ?

The maximum value of determinant |{:(cos(alpha+beta),sin alpha,-cos alpha),(-sin(alpha+beta),cos alpha, sin alpha),(cos 2beta,sin beta, cos beta):}| is ___________

(sin^(2)alpha-sin^(2)beta)/(sin alpha cos alpha-sin beta cos beta)=tan(alpha+beta)