Home
Class 12
MATHS
If alpha = cos^(-1)((3)/(5)), beta = tan...

If `alpha = cos^(-1)((3)/(5)), beta = tan ^(-1)((1)/(3))` , where `0 lt alpha, beta lt (pi)/(2)`, then `alpha - beta` is equal to

A

`cos^(-1)((9)/(5sqrt(10)))`

B

`sin^(-1)((9)/(5sqrt(10)))`

C

`tan^(-1)((9)/(5sqrt(10)))`

D

`tan^(-1)(9/14)`

Text Solution

Verified by Experts

The correct Answer is:
B
`cosalpha=3/5sinalpha=4/5`
`cosbeta=3/(sqrt(10))sinbeta=1/(sqrt(10))`
`sin(alpha-beta)=sinalphacosbeta-cosalphasinbeta`
`12/(5sqrt(10))-3/(5sqrt(10))=(9)/(5sqrt(10))`
`alpha-beta=sin^(-1)((9)/(5sqrt(10)))`
Promotional Banner

Similar Questions

Explore conceptually related problems

If alpha=cos^(-1)((3)/(5)),beta=tan^(-1)((1)/(3)), where 0

If sin alpha=(3)/(sqrt(73)),cos beta=(11)/(sqrt(146)) where alpha,beta in[0,(pi)/(2)] then (alpha+beta) is equal to-

If tan alpha=(1)/(7) and sin beta=(1)/(sqrt(10)), where 0

If sin(alpha+beta)=1,sin(alpha-beta)=(1)/(2) where alpha,beta in[0,(pi)/(2)], then tan(alpha+2 beta)tan(2 alpha+beta) is equal to

If cos(alpha+beta)=3/5, sin(alpha-beta)=5/13 , and 0 lt alpha, beta lt pi/4 , then tan(2alpha) is equal to:

" If cos(alpha+beta)=(3)/(5) sin(alpha-beta)=(5)/(13) and 0< alpha, beta < (pi)/(4) then tan(2 alpha) is equal to

If alpha=tan^(-1)(tan(5 pi)/(4)) and beta=tan^(-1)(-tan(2 pi)/(3)), then 4 alpha=3 beta(b)3 alpha=4 beta(c)alpha-beta=74 alpha=(3 beta)/(12) none of these