Question

If `cos(alpha-beta)=3sin(alpha+beta),t h e n1/(1-3sin2alpha)+1/(1-3sin2beta)=` `1/2` (b) `(-1)/2` (c) `1/4` (d) `(-1)/4`
A. `(1)/(2)`
B. `(-1)/(2)`
C. `(1)/(4)`
D. (-1)/(4)`

Answer 1

Correct Answer - D
Put, `beta=0rArr tan alpha=(1)/(3)`
`rArr sin 2alpha=(2((1)/(3)))/(1+(1)/(9))=(3)/(5)`
`therefore (1)/(1-3sin 2alpha)+(1)/(1-3sin2beta)`
`=(1)/(1-3sin2alpha)+1=(1)/(1-(9)/(5))+1=(-1)/(4)`.