Home
Class 12
MATHS
If 0 le alpha, beta le 90^(@) and tan(al...

If `0 le alpha, beta le 90^(@)` and `tan(alpha+beta)=3` and `tan(alpha-beta)=2,` then value of `cos 2 beta` is :

A

`(7)/(5sqrt2)`

B

`(1)/(5sqrt2)`

C

`(7)/(-5sqrt2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`tan2beta=tan{(alpha+beta)-(alpha-beta)}`
`=(tan(alpha+beta)-tan(alpha-beta))/(1+tan(alpha+beta)tan(alpha-beta))=-(1)/(7)`
`rArr 0 lt 2 beta lt 90^(@)" "(because tan 2beta gt 0)`
`therefore cos 2beta=(7)/(5sqrt2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

If 0<=alpha,beta<=90^(@) and tan(alpha+beta)=3 and tan(alpha-beta)=2 then value of sin2 alpha is

If 2tan alpha=3tan beta then tan(alpha-beta)=

If alpha+beta=90^(@) and beta+gamma=alpha then tan alpha-tan beta=?

If alpha+beta=90^@ and alpha=2beta , then the value of 3cos^2alpha-2sin^2beta is equal to:

If sin2 alpha=4sin2 beta, show that 5tan(alpha+beta)=3tan(alpha+beta)

If tan (alpha-beta)=(sin 2beta)/(3-cos 2beta) , then

If 3 sin alpha=5 sin beta , then (tan((alpha+beta)/2))/(tan ((alpha-beta)/2))=

If 3 sin beta=sin(2alpha+beta) , then tan (alpha+beta)-2 tan alpha is

If 3sin alpha=5sin beta, then (tan((alpha+beta)/(2)))/(tan((alpha-beta)/(2)))=